Not to say it's a bad idea but:

Battery life. it's pretty bad as it is and having the Wifi on constantly would only drain it more.
It's a games console not a phone. People use the psp to play games not to communicate. That's what a phone's for.
Flash space. The flash is full as it is. I don;t think many more features would fit. Remember location free player had to be removed at one point to fit CFW on.