When Liza Lutzker threw her daughters a back-to-school party at the Berkeley Rose Garden, she and her husband packed all the provisions on their electric cargo bikes: two boxes of firewood, food for 30 people, a water dispenser, plates, napkins, glasses and two kids.

Then they rode 2 miles from their home on Milvia Street to the terraced amphitheater on Euclid Avenue, high in the leafy-green hills. Six years ago, Lutzker would have hauled everything in a car. Now she travels almost exclusively by foot and bike.

Her family illustrates a culture shift in the Bay Area, where e-bikes, once conceived as a luxury item, are becoming a widely accepted form of transport. Enthusiasts view them as an option for commuters or for weekend warriors who want speed and distance with less work. In the case of cargo e-bikes, they’re a solution for the types of trips that suburban parents once made in minivans: grocery shopping, school drop-off, shuttling kids to soccer games — even getting to BART, which has begun filling its parking lots with housing.

The trend is picking up globally, though it’s become particularly noticeable in Marin County, Berkeley and San Francisco. That pleases e-bike riders and merchants, even as it highlights the deficiencies of local roads, where collisions are frequent and some bicycle lanes are marked only with a picture of a bicycle.

In December, research and auditing firm Deloitte predicted that 130 million e-bikes will be sold internationally from 2020 to 2023. By the end of the year, these motor-powered devices will outnumber other electric vehicles on streets and roads, said Paul Lee, global head of technology, media and telecommunications research at Deloitte.

This surge has emboldened people like Rob Allen, owner of Blue Heron Bikes in North Berkeley. Since opening the store in 2012, he has increased his stock of electric bikes from one to 50 and steadily tried to debunk the myth that distance cycling is solely for a rarefied group of athletes.

“There was this perception that you can’t ride far without pretending you’re a bike racer — that you have to wear some type of aerodynamic outfit,” Allen said. That’s no longer true; he and others noted that with the advent of electric-assist motors that kick in after a person starts pedaling, it’s become easy for elderly people to surmount hills or for office workers to ride to business meetings. Many of Allen’s customers are families seeking to shed a car.

But the e-bike renaissance faces challenges. Mainly, infrastructure. Many streets lack protected bike lanes — or even painted bike lanes — and bike injuries and fatalities in San Francisco and other cities remain a stubborn problem. Secure parking is scarce. Not everyone has a private garage to store an e-bike, and the vehicles are too heavy to lift up flights of stairs. Some BART elevators are too small for larger e-bikes, which inhibits people from taking them on transit. Cost is an issue: At $3,000 to $5,000, they’re too expensive for many people.

Then there’s the social aspect. Even as more parents, families and commuters gravitate to e-bikes, many other people still see cars as a way of life.

“We’ve been a very car-oriented culture, and there’s a lot of inertia (toward) changing your daily life patterns,” said Berkeley transportation planner Tom Lent. “Bikes have been considered toys more than a useful form of transportation.” One hurdle for the electric versions is “getting people to take them seriously.”

The barriers seem steeper in low-income neighborhoods that tend to be far from the urban core.

Najari Smith, founder of the Rich City Rides bike nonprofit and worker-owned shop in Richmond, said his workers keep several e-bikes in stock. In January, they had a few models priced from $1,000 to $2,000, about half the cost of an average pedal-assist bicycle. Among them: an e-tricycle that could be outfitted to carry groceries, and a couple of Espin electric bikes, each equipped with a mid-drive motor.

A cycling evangelist who leads Sunday rides and camping trips for kids, Smith sees the potential of e-bikes to cut pollution, get cars off the road and convert the uninitiated. Richmond is a working-class city where bikes are starting to catch on as a lifestyle choice, particularly with the Greenway, which curls along the waterfront, and the Bay Trail, which feeds the Richmond-San Rafael Bridge bike path. Some activists pitch electric bikes as an alternative for teachers, food service workers and janitors making the hellish commute from Contra Costa to Marin County.

Still, Smith understands why someone with a tight budget might choose a car instead.

“I hate it when people who still kind of embrace car culture get demonized, because there are a lot of class dynamics with that,” he said. “We have e-bikes for $1,000, but you can find a used car for $500. And I’ve met folks for whom a car is another place to live.”

In San Francisco, where City Hall leaders are bullish about reducing automobile traffic and building protected bike lanes, many residents have gravitated to e-bikes. Ed Parillon is one of them. After “a lot of hemming and hawing,” he bought a cargo e-bike last summer — race car orange, with a double seat in back to carry his two children to school. It’s small enough to store in the basement of their 700-square-foot cottage in the Mission District.

“I’ll take them to school and back, and then if I need to pick up groceries or dog food, or take stuff to the UPS store in Bernal Heights, I’ll do that too,” Parillon said.

He represents a new subset of bike advocates in the city — parents with errands to do, shopping lists to fill and two kids to drop off in the morning, who then don’t want to be stuck driving to work in a car. Often, people considering a purchase would test drive the rental e-bikes from Jump and Bay Wheels. Riders who fell in love with the pedal-assist two-wheelers are now buying their own.

“E-bikes are just so nimble,” said Paul Supawanich, transportation adviser to Mayor London Breed. He envisions a future in which these devices could be instrumental for parcel delivery or for companies such as Postmates and DoorDash. Gig workers in New York have traded cars for electric bicycles, a transition that’s helped unclog city streets.

“Is a vehicle that can carry four passengers and a trunk really needed to deliver takeout Chinese?” Supawanich asked. He and other policymakers have become fixated on tailoring mobility to meet “the size of the trip.”

That idea resonates with Lutzker. She and her husband use a cargo e-bike for just about everything: trips to Tilden Regional Park, hauling their daughter’s cello to a music lesson, transporting a desk that they found on the street and attached to the bike with bungee cords. They’ll pedal the kids to school in a downpour, placing a waterproof backpack cover over the seat cushion to keep it dry.

On weekday mornings in Berkeley, the streets are full of parents on cargo e-bikes, Lutzker said. Occasionally, they’ll encounter opposition. Every once in a while, a driver will yell at Lutzker from a car window, scolding her for “carrying my kids like that.”

She ignores the criticism and keeps riding.

Rachel Swan is a San Francisco Chronicle staff writer. Email: rswan@sfchronicle.com Twitter: @rachelswan