In my experience with my first motorized bicycle, these are the weaknesses I've observed:
First and perhaps most important, the brakes. I have a 70 cc HT engine mounted to a 14 year old Trek 820 mountain bike. It has the center pull cantilever brakes on it. With my 44 tooth sprocket, I can get it going fast enough that it will not stop quickly and in a safe manner.
Tires. Bicycle tires are not made to go faster than (I'm guessing) 40 MPH. I've once gone as fast as 50 MPH (Without engine, downhill on Skyline Drive in the mountains in the western part of Virginia. More exciting than a crotch rocket.) There are tires for bicycles that are rated at something like 70 MPH, but I can't remember what they are called or who makes them. Maybe Google can remember.
Wheels. They just aren't heavy enough. I could taco a rim so fast... the bearings aren't really made for high speeds either. They would heat up, thin out the grease, which would cause more heating. You'd likely not have a failure the first time going too fast, but after a few heating-cooling cycles the metal would fatigue and start to crack. Not to mention the axle could lose it's temper and get soft.
A lot of motorized bikes (Including mine) don't seem to have suspension on both wheels. When you get going fast enough, you need your wheels to be able to track the ground better. You don't want to just hit the high spots, and you don't want it to shake around so much you get thrown off.
Last, but not least: Police. If you've got your motored bike flying about at 70+ MPH on the highway, or even 45 on a street, you greatly increase the amount of attention you will get. That's not good. It's a novelty to see a bike with it's own engine. (Especially around here, I have THE ONLY ONE.) We don't want it to be a nuisance.
Can anybody think of anything I've left out??
-Mark