I still have my Axim, and I still use it too, although I haven't played games on it in a long while. They never seemed to progress to a level comparable to the GBA, or even the GBC, really. Not enough money behind it. Now, I don't even know where they sit. Has everything moved to cell phones? I know some PDAs have cell phones built in, but I can't imagine using something that size and shape as a phone.
Also, did id Software really get into this market? It seems way odd. I can see some hungry third party negotiating with them to get the IP into phones, but not Carmack and company.