How can I replace a carrier-customized system with the original version?
It might be possible in some cases (I know Sony has released blobs before for ROM devs to use), but generally OEM's have agreements with carriers and release only carrier-laden ones. I know you said "without rooting", but you could technically flash a custom recovery and from there flash a "de-bloated" stock ROM from another developer. I know it's probably not really what you mean, but it does technically avoid rooting :P. That's probably going to be your best bet. Another, more ad-hoc option would be to freeze carrier apps (via titanium backup or something similar), and/or use alternative launchers like Nova or Apex to hide them from your app drawer. I don't think you need to be rooted to freeze an app, but I could be wrong. I feel your pain though, had an HTC Evo 4G back in the day. Never have I ever cared less about Sprint's sponsorship of NASCAR.