If it were a simple changing of the CPU clock speed, like Wii U -> Wii -> Gamecube, then it would be silly not to. But with the Xbox going from x86 to the 360's PowerPC and now to x86-64, it's definitely more trouble than it's worth. After a year or so, no one will care anyway.
The 360's backwards compatibility was something they shouldn't have bothered with as it often didn't work properly and had so many limitations that even if the game "worked", the 50/60Hz thing usually stopped you playing on an HD TV anyway.
One thing I would like, that may be possible, is downloadable original Xbox games, like PSN's PS1 and PS2 Classics range. I know a lot of the best Xbox games have been re-released in HD and rights issues will probably prevent a lot of others being on the service, but there are a few rarer Xbox games I would like to get hold of.
"You're giving me Asari Commandos? You're the best father a girl could wish for!" - Liara T'Soni