We didn't need a license, by virtue of the displacement of the stock engine being small (IIRC the limit was 125cc? Or maybe even less). They also had to have pedals, so small motorcycles or vespa-style scooters did require a license. Or at least a registration.
The mopeds would barely go 30mph as sold. That was hackable though if you were so inclined and had a set of wrenches.
Yeah 49cc mopeds that aren't registered appear to still be a thing where I am (Boston). And I think it's 49cc 2-stroke so equivalent to like a 90cc 4-stroke (whether that ends up violating a different emissions rules, I don't know).
Still, parking is such a racket in Seaport, including unnecessarily strict ticketing on motorcycles, that I don't blame the delivery guys for using the mopeds. I'm not sure what their realistic alternative would be.