Cars do have more utility than motorcycles, but where I live (college town in American midwest) there are many poor people who drive small, cheap motorcycles. Speculation on why:

<50cc scooters are subject to different -- usually lower -- registration, insurance, inspection, and licensing requirements than cars.

State-minimum insurance for my cheap (KBB ~$1000) used (+200K miles) car would be about $700/year. Similarly minimal insurance for a 2010 Honda Ruckus would be $100/year. (I just checked Geico.)

Small motorcycles consume a lot less gasoline than cars, especially old, cheap ones being driven in-city.

Spare parts for scooters can be purchased and shipped cheaply, and assembled in a minimum of space with cheap hand tools.

Scooters don't require a full parking space to store. They can be stashed against signs, at bike racks, next to doors, in tiny alleys, or any other free spot. Living with other people? You don't need to worry about blocking the driveway, or being blocked yourself. Work downtown? You can get away without buying a pass at a parking garage.

The number of places in the US where the situation you mentioned is reasonable and public transit is not also good enough to go car-less is very small. Carrying groceries on a moped is doable but a pain. Commuting on one in the winter isn't exactly fun either. Carrying kids on a scooter is a great way to meet every cop in every place you drive through. I wish mopeds were more practical but there's a bunch of little reasons that add up to them not working as well as a cheap car.... which is why pretty much nobody around me except a bunch of single people under the age of about 25 rides them.

Everything you have said is generally true. My point is that there are scooters driven where I live, that most of them are driven by low-income people who are in the presumably-uncomfortable position of a scooter being their best option, and that noise regulations would be an indirect regressive tax against them.