Are the motor scooters the kids ride on today legal for use on public streets?

The quick answer is NO.

Does it have:
Headlight?
Taillight?
Brake Light?
Turn signals?
Mirrors?
A place to attach a tag?
A registerable title?
At least a 50cc, 4 stroke engine?

All required for a street legal vehicle.
If you got it from an auto parts store, it's not street legal.

only ones with lic plates are legal for street use

Yes, but not scooters that look like motorized skateboards.

it depends on the location you are living in.

Yes, but most states don't allow scooters with an engine size less than 150 CCs on a highway or freeway.