Ah! But you can! It needs proper inlet valves, but you can, and if you're using direct fuel injection, you can use it on an ordinary 2 stroke to completely scavenge burnt gases from the cylinder.
arctic cat snowmobiles have been selling turbocharged two stroke snowmobiles for years. what they do is tune the pipe for the same rpm that the clutch locks at, that way the exhaust pulse from the expansion chamber acts as your exhaust valve. while it is alot harder to do, you can turbo a smoker, but it will have a narrow power band, which is why you have to use a CVT and tune for the rpm of your CVT
There is a company somewhere making a 4 cyl 2 stroke diesel aero engine, no ports, all valves in the head, and I would presume, a lot of scavenge air being blasted through. For the 2 stroke to achieve it's full potential, people need to accept it will have a 4 stroke level of complexity.
Chevy used a two stroke diesel, they would not run with out a supercharger or turbocharger, the intake was ports at the bottom of the cylinder with valves up top, but with out some forced induction there was no way to scavenge the cylinder. http://www.youtube.com/watch?v=lcBiCyX9lnk
variable exhaust port geometry solves all of the issues of running a turbocharger on a 2-stroke, like a rehashed version of the Yamaha YPVS system, but you wouldn't be able to purchase your Chinese bicycle engine kit for $200.
Direct fuel injection would also solve most of the emissions problems with a turbocharged 2-stroke.
The technology exists to solve all the problems, just that it doesn't come cheap!
You can still build a simple 2 stroke that accepts supercharging. It would be a split single. 2 cylinders normally working off the same crank throw, bores parallel, and sharing the cylinder head. One cylinder then runs slightly ahead of the other in the rotational cycle, and functions as an exhaust valve.
This gives diagrams of different ways to do the same job.