San Franciscans will almost certainly be asked a groundbreaking question on the November ballot: Should all city residents be guaranteed the right to quick, effective mental health care?

It’s clear the city’s mental health care system is devastatingly broken. We’ve all seen mentally ill homeless people released from San Francisco General still wearing their hospital gowns wandering into traffic or screaming at nobody in particular.

But there are also many San Franciscans who struggle with depression, anxiety and other mental health issues in a more private way. They have housing, jobs and medical insurance, but still can’t get the treatment they need. Just this month, for example, thousands of mental health clinicians at Kaiser voted to authorize a strike if staffing levels aren’t boosted to ensure patients can get quicker mental health treatment.

People at both ends of this spectrum — and every San Franciscan in between — would be covered under a proposed program called Mental Health SF. It’s a twist on the 12-year-old Healthy San Francisco program, the first of its kind in the country, that ensured medical care for nearly every city resident. The proposal would expand the promise to ensure mental illness and addiction are also covered. Its backers say it would likely be the most comprehensive approach to mental health care in any American city.

It’s the, well, brainchild of Supervisors Hillary Ronen and Matt Haney and also has support from Supervisors Gordon Mar and Shamann Walton. They’ll introduce the proposal at the June 4 meeting of the Board of Supervisors and ask city voters in November for their approval. The measure would need just a simple majority.

In a city with huge income disparity, they’ll attempt to fund the operating costs with a new gross receipts tax on those companies that pay their CEOs upward of 100 times more than the median compensation paid to employees. That proposal, probably on the November or March ballot, would need the support of two-thirds of voters.

In a city that once embraced big, creative plans, this is a refreshing idea. From Healthy San Francisco to same-sex marriage to free City College, City Hall has long backed innovative ideas. But not so much when it comes to mental health care and drug abuse — at least not lately. (City officials do support opening a safe-injection site, but are waiting for state approval — and its opening, if it happens, is still far off.)

Our so-called progressive city has become so paralyzed in this arena, it has allowed our sidewalks to turn into de facto psychiatric wards and injection drug sites. While City Hall plays around the edges, adding some treatment beds here and creating a new high-paid position there, the misery festers.

“San Francisco has the opportunity to lead, to say, ‘This should be a right for everybody.’ We’re going to build a system around it,” Haney said. “It’s going to be messy as we figure it out, but we have to figure it out. We have the values. We should have the resources. We just need the leadership.”

Granted, it’s a big dream, and one with many kinks to work out. For example, only those well enough to know they need treatment would be cared for under Mental Health SF, but more on that later.

Mental Health SF would center around the construction of a new treatment center, probably on the campus of San Francisco General Hospital, that would be open every day, around-the-clock. It would open by June 1, 2022. Ronen and Haney said they don’t know how much construction would cost, but have asked Mar to commit half of the revenue from his IPO tax, also pegged for November, to build it. Mar has estimated the tax would raise between $100 million to $200 million in the first two years.

Any city resident needing mental health or substance abuse treatment could walk in and receive quick access to psychiatrists, nurse practitioners, case managers and a pharmacy. There would be an acute crisis wing with beds for those who are so ill that they can’t safely be released.

Patients would be divided into two categories. “Bridge patients” would be those with private insurance or Medi-Cal who are having a hard time getting an appointment with a psychiatrist or a prescription written. The treatment center would help them and seek reimbursement from their insurance company.

“Core patients” would be those newly released from jail, uninsured people or others who need longer-term care provided by the city. Both sets of patients would be paired with a “navigator” who would help them obtain the care they need.

Mental Health SF would also create a new Office of Coordinated Care within the Department of Public Health to better link all the disparate treatment facilities and a working group to figure out how to expand treatment beds throughout the system.

The plan’s backers say it would cost the city an estimated $40 million to $60 million annually to staff the center and the Office of Coordinated Care. The idea is to pull in additional federal dollars for substance abuse treatment and state Medi-Cal funds. Assemblyman Phil Ting has signed on to help find ways to direct more state money to the project.

Ronen and Haney said they’re hopeful the program would actually save money in the long term, which isn’t too far-fetched considering the Department of Public Health spends $370 million annually on mental health care and substance abuse treatment.

While any additional taxes to pay for the program would need voter approval, Ronen and Haney don’t have to go to the ballot just to create Mental Health SF. But because they are so disenchanted with the Department of Public Health’s performance, they want a binding mandate from voters.

Grant Colfax, the new director of the Public Health Department, said he hadn’t yet seen the proposal and couldn’t comment. But he has said that he knows much needs to change. For example, his department says it serves 30,000 mental health patients yearly — and yet so many are still on our streets in obvious distress.

“If we keep doing the same things we’ve been doing, then we’re not going to address this gap,” Colfax said in April.

One clear problem: There’s too little follow-up. Even many of those brought by police to San Francisco General Hospital for a 72-hour hold because they pose a danger to themselves or others don’t get care after they’re discharged.

Staff in the cramped, dingy psychiatric emergency room — which is licensed for just 18 beds — have called it a “car wash” because they quickly clean up patients before sending them on their way.

For those voluntarily seeking help, there is no central waiting list for care, and patients and their families must seek out information from each clinic or treatment facility on their own. The Department of Public Health has no centralized tracking system to monitor all the nonprofits and city programs providing treatment.

If patients do receive care, there are too few beds at every step of the system. For example, 44% of patients released from 90-day residential treatment facilities are sent back to the streets where their mental health problems and drug addictions are likely to resurface.

“The system is completely broken, and it’s a mess,” Ronen told me. “Not only does the Department of Public Health not admit there’s a problem, instead of spending their time generating a vision and a plan to fix the system, they’re spending all of their time trying to hide the fact that there is a problem.”

To be fair, Ronen hasn’t supported San Francisco Mayor London Breed’s push for expanded conservatorship, which would allow the city to compel more seriously mentally ill and drug-addicted people into treatment. The Mental Health SF plan would only help those who are well enough to know they need help. Still, Ronen said she could envision police officers using the treatment center as a carrot as opposed to the stick of jail time for mentally ill people or those on drugs caught committing low-level crimes.

It seems like the system would be improved if the ideas were paired — mandate treatment for those in clear crisis and offer quicker care for them and everyone else.

Also, Ronen and Haney haven’t done much about the city’s tacit acceptance of injection drug users shooting up on our sidewalks. They said the city shouldn’t permit it and that drug users, too, can come to the treatment center and receive help. But it will take action from the supervisors and mayor to change the culture of blatant drug use on our streets.

Steve Fields is the director of Progress Foundation, which operates treatment facilities for mentally ill people, and has been working on improving our mental health system for 40 years. He said the Mental Health SF idea has been “germinating for a long time, but has never come to fruition.”

He said while many programs offered by the city are excellent, their coordination and coherence is poor. Patients can’t easily gain access or even figure out how to get on waiting lists or how long those lists are.

“The idea of a triage services center is as good an idea as I’ve heard for providing that kind of coherence,” he said. “Clients know they can show up and get immediate services.”

He said the ambitious plan could be a game changer. Goodness knows we need one.

San Francisco Chronicle columnist Heather Knight appears Sundays and Tuesdays. Email: hknight@sfchronicle.com Twitter: @hknightsf