Thats curious
Just having apps installed shouldn't slow it down, and iOS is pretty brutal about shutting them down when they're not in the foreground, this must be down to something essential thats always running and doesnt scale.
My money is on the Springboard, It was only designed for 20 apps, but now you can stuff almost ten times that to each of its ten pages. I suspect it caches all the icons and those 'previously' launch shots into RAM so there is never any lag on the homescreen, but one (hundred) too many apps and the system starts to get light headed from RAM starvation.