Yeah, with enough time and effor you just might. But consider this: Windows has a ready operating system, software and settings that work with the cellphone. You have a guarantee it works. If you just blindly went and "installed" Linux on that cellphone, your warranty and guarantee would be void, you would probably end up with an unusable thing (unless somebody has already created a fully functional and tested OS that runs on your cellphone and can actually do something with it's hardware). To create an operating system for a cellphone isn't impossible, but certainly takes time and isn't as easy as eating a pie (or if it was, why are 99,9999999% of the cellphones on the market completely buggy, and doing a firmware upgrade often just makes things worse, even though that software should be made by "professionals"?)
Shortly said, I don't recommend. By the time you had something working on it (you could call, for example, or type a sms and maybe even send it) the phone was too old to use, it's battery dead and the whole GSM technology (or whatever it uses) history
that's (one reason) why big companies create cellphone software and there aren't much, if any, open source alternatives around.
An example: you can install Linux on
some of Apple's iPods. This is because they're pretty standardized and somebody has taken the time and effort (it's not a brand new project). And still not every iPod out there works with the thing. When you consider cellphones, they're far from standards, they're many, new ones come out every day and a two-year old cellphone is considered something you find in Jurassic Park. If somebody had the time and intentions to start coding an open source, possibly Linux-based, OS and software for a cellphone it wouldn't go far because it would only work on a small range of phones, and possibly was too old by the time it was "ready" or even "beta" (those cellphones wouldn't be sold anymore I guess, they go off the market so soon). And it's not just getting the OS run on the cellphone: in addition you need a lot of software to handle calls, different kinds of messages, data transfers, settings, addressbook, ... that's a whole lot of work. Compared to iPods, on them the main thing is to play music (for which there is more or less ready software available) and in addition to that some extra things like small games, video or recording.
If you're interested in creating software for cellphones I don't think Windows Mobile is the thing for you. It could be, but I guess you can start more easily by taking a phone with Symbian inside and starting to create programs for that -- there are a lot of instructions, books and stuff for Symbian cellphones.
EDIT: each and every single piece of cellphone software, including operating systems, suck nowadays. In my opinion the gratest reason is that the phones are created so rapidly, sold rapidly and dumped rapidly, so software designers, programmers and testing staff don't simply have enough time to find out nearly all -- or even the greatest -- bugs from the phones before they're released and forgotten. Compared to the old cellphones (those without a colour screen or anything fancy) every new cellphone is buggy and "sucks" like you said. The problem persists because the market needs to sell those phones more rapidly every day, leaving less and less time to program the cellphones well -- some examples are far from good, from time to time I wonder how anybody can even use them (the thing may freeze just because you pressed the button too quickly, or for no apparent reason). If you want a cellphone that doesn't suck, you're going to have to find a brand new 5-10 years old thing, and in addition a battery for it (which may provide a difficult task, especially the battery, if you want one that still works).