Tons of reasons:
1) I don't want to have to deal with any of the BS roadblocks the carriers put in place to prevent unlocking a phone (encrypted bootloaders), or having to rely on security exploits to gain root. Each phone is a different circumstance, requiring waiting, reading forums, and other crap I don't want to deal with.
2) I don't want to deal with dumb design decisions of other phones like including a hardware menu key.
3) I don't want to HAVE to load a ROM from day one of ownership to be able to use AOSP. With a Nexus, if I don't feel like messing with the phone, I don't have to, and I'll still have a pure AOSP experience without bloatware or other crap.
4) As others have said, just because you can load a ROM doesn't mean you'll have a great experience. There will be bugs, especially with CDMA devices, and you will inevitably end up spending hours on XDA researching some problem or another. Far too many people say "use a ROM" as a solution to everything - it isn't. Nexus phones, OTOH, have all of their sources available so devs can make the best ROM possible for them, and the most quickly. It's your best shot at having a trouble-free experience without digging around on forums.
Better question is, why NOT use a Nexus device? Why sign up for a carrier's overpriced contracts and locked down phones? A spec or two might be better, who cares, that stuff changes every few months. I have no interest in paying $80-$100/month for my cell phone bill. The only argument I have seen is if you need Verizon coverage in your area.