Sounds more like a discussion about retention vs no retention.

Fixie straps are Velcro adjustable and allow retention with a variety of shoe types, but
I’ve never tried them. They’re $20-30 online.

I’ve never tried clipless, but I did use clips/straps briefly a year ago - cheap plastic ones with nylon straps - but they were too small, and increased complexity/difficulty with “marginal” gains (zero), well, end of experiment.

Regarding speed? You’d have to be riding pretty hard in the first place for foot retention to make any speed/time difference. I doubt most commuters are trying to shave seconds off their commute. Those using commute for training for racing are already using retention. Those trying to shave seconds off their commute NOT training for racing - I mean, if getting to work faster is your goal, the bike may not be the best tool.