Well that's your choice...
Yes, I have registered one in Florida... In Palm Beach County.... After the initial paperwork, it takes about 2 weeks for them to set you up with an appointment to have it inspected.. (They inspect it and then give you a VIN number/sticker.)
Once inspected, all you have to do is go to the DMV and pay the $50ish bucks for the registration.
You CAN build a small motorcycle, but at that point, it is probably WAY easier to just buy a scooter.
You DO have a license, right? Or is that your "main area of contention"? Because that's a lot of people's reason for having an issue with building one.
The registration for a moped is soooo much easier than one for a motorcycle and is a lot cheaper.
Yes, I do have a license. I also have multiple small motorcycles I have built (on old frames, like my '72 Trail 70 for example) that are way cooler, more capable, faster and get better gas mileage than any stupid scooter with its power-robbing belt drive and engine mounted on the swingarm. Did I mention that I hate scooters? Also, the typical small motorcycle I build costs less than a Chinese scooter, and only costs about $20 to register in my state. Liability insurance costs me about six dollars a year.
I'm not building motorized bicycles because I have no other form of transportation. I build them because I'm a gearhead, and because most states don't require all the registration nonsense on something so slow and light. Georgia for example, doesn't require registration on even a 50cc motorcycle, with gears and everything.
Florida obviously hates motorized bikes. That's why they were flatly illegal until fairly recently, when they smugly condescended to make them legal, but only if you spend a large percentage of what the bike costs to build, and jump through hoops to register it. Why? Is it such a menace to public safety? No. Because Florida is such a police state that they can't stand not having their hands in everything possible.
Motorized bicycles aren't the only thing Florida tries to prohibit that freer states don't hassle with, either.
I occasionally visit and camp there, but I'm glad I don't live there. If I did I would probably take myself and my tax dollars, and move to a freer state.
I forgot to mention: you describe a process of inspection, fees and registration, and then claim that it is "soooo much easier than one for a motorcycle." Wow. I can register a 300cc motorcycle with a 35+ year old frame for $20, a bill of sale, and no inspection. Anyone (including a Florida resident, btw) can register a sub-300cc motorcycle in Vermont, via mail, with only a bill of sale (no title required on sub-300cc even if brand new) for $44. And as I mentioned, Georgia doesn't even require registration of a full-blown 50cc motorcycle.