Seems to vary across models. Googling for Honda Civic: "And the Low-Speed Follow function can bring the vehicle to a complete stop when a vehicle detected ahead slows to a stop, and it lets you resume operation by pressing a button or the accelerator."

Many cars do have “stop-and-go” assist, including lane centring, meaning the car will maintain distance to the car in front down to 0 while maintaining its position in the centre of the lane, and then accelerate from 0 when traffic starts moving again. This is a relatively new feature, being generally available on luxury marks from ~2016 or so. Many cars with ACC prior to that wouldn’t engage below some speed, but would continue operating down to nearly 0 or 0, and then require the driver to take over until the engagement cutoff speed was reached. Some cars as far back as at least 2012 supported this (that I’ve driven), possibly older as well.

Or at least, driving at very slow speeds with no pedestrians around doesn't require much attention.