You probably didn't have speedier options in 2005 that wouldn't make the system much more expensive. Also with the console being a loss leader and profit expected to come from game licensing, it was judged to be worthwhile at the time.
> Maybe that's why Microsoft could never make a PSP or a Nintendo handheld type console
I'm fuzzy on the history but I do believe online play was embraced by Microsoft far before Sony or the others. Am I right? Anyway, that required home Internet. Sony/Nintendo had their popular portable systems - designed for offline play. In 2005 that type of Internet-reliant online gaming wasn't going to work too well on a portable device with 2005-era wifi and 2G expensive cellular plans in the fashion that Sony or Nintendo would envision.
Also in 2005 Microsoft's mobile plans were all-in on Windows CE. Because their strategy at time was Windows everywhere...why? fundamentally Microsoft was at that time primarily software licensing company that would rather sit and collect license royalties and let other companies develop the low-margin hardware side. Could you imagine a clunky Xbox Portable Zune CE, being really some rebranded Toshiba or Sharp device that was something else in Japan?