SneakySnake hit the nail on the head. What I want to know is why any given handset, in this case the Xperia Play, will run Android 2.3 smoothly but not Android 4. Android 4 was meant to be a major step forward in efficient resource usage but it appears to be the opposite - every new version needs faster hardware to produce acceptable performance.
I don't believe the excuse for not giving the Xperia Play the update though. Up until the Xperia S, Sony haven't been using dual core processors, and only the Xperia Ray and Xperia Arc S were even using high clock frequency single core processors. Everything else is using the Qualcomm QSD8x50 (1GHz Scorpion CPU core with Adreno 200 graphics) or MSM8x55 (same but with Adreno 205). Every other handset in that list has the same specs as the Xperia Play.
Xperia Play: MSM8255 with 512mb RAM
Xperia Arc: MSM8255 with 512mb RAM
Xperia Neo: MSM8255 with 512mb RAM
Xperia Mini: MSM8255 with 512mb RAM
Xperia Mini Pro: MSM8255 with 512mb RAM
Xperia Pro: MSM8255 with 512mb RAM
Xperia Active: MSM8255 with 512mb RAM
I don't know whether manufacturers are lying about how much muscle is required to run ICS smoothly (certainly looks to be the case with Sony) or if Android 4 really does need serious muscle to run smoothly. Either way, whatever phone replaces my crappy HTC Wildfire (2.2), it sure as hell won't be any kind of Android.