When HubSpot Inc. brought high-end coffee to its Cambridge, Mass., campus, it expected employees to be thrilled. Facilities head Ken Papa created a “coffee garden” with an array of self-service brewers, grinders and two cold-brew taps—all free of charge to employees. The software company already had a gym, mobile bike repair shop and visiting yoga and barre instructors.

But the cold brew taps proved so popular that workers griped they often ran dry. An unknown employee created a website, does2canhavecoldbrew.com, to monitor...