One problem with fuel injection above the piston is pressure control..
Fuel is pushed through a fuel injector under some amount of fuel pressure. This amount of pressure PLUS the time the injector is open regulates exactly how much fuel is delivered.
Now if some opposing pressure is pushing against the injector, the injector needs more fuel pressure behind it (or it needs a longer open-time) to provide that correct amount of fuel.
Pressure in the chamber above the piston is high and it constantly varys.. and this pressure resists the fuel pressure.. so fuel delivery is very difficult to control.
Another stumbling block is the tip of the injector cannot withstand the heat of combustion. Wherever it's mounted must be behind some protective barrier.
Honda and a few others have experimented with it.. but by the time the system is working, it's so complex and so expensive it makes the main advantage of a 2-stroke (simplicity) pointless..