Aprilia Direct injection 2 strokes. Turbo's too?

Right ive been thinking, now that 2 strokes are Di like the diesels it doesnt matter about compression and knocking as much as it might have. Wouldnt it be possible now to have a turbo to squeeze more power out of them while also doing away with large exhausts and the noise as they wouldnt be needed to pull more air into the chamber as its being pushed in... They could id imagine even make them sound like high reving 4 strokes not like wailing monsters. Maybe they would even gain a bigger power band. 2 stokes could take over the world mUHA HA HA

Am I chatting crap or am I on something here?