Yeah, because we never ran "full blown, mature OS" on our PCs when they only had 4MB of RAM and 20 MHz CPUs. :rolleyes:
The PSP is more than capable of running a full blown, mature OS - there's just no reason for it. The PSP is meant to play games, and play multimedia. You don't need a full blown, mature OS to do that.
As an example, I run MacOS 8.1 on my PSP via Basilisk II. That is a full blown, mature OS. Maybe not modern, but you didn't specify modern, did you? ;) So if we can run a full blown, mature OS in an EMULATION on the PSP, you can certainly have a full blown, mature OS natively on the PSP.
Even if you specify modern OS, the PSP is more than capable of an OS the same level as Windows XP, just with a couple features missing - like memory protection. Such a thing really isn't needed on the PSP anyway.