The original xbox and xbox 360 should keep alive through the years

bringing those networks up to code would be mammoth task, also a lot of the games were on the developers servers and not xbox and most of them are now shutdown forever and will never come back.

making games backward compatable is not that easy, they have wrap the gam in an emulator customised ofr that particular game to make it run, this takes time and resources. They also need permission from the developer/publsiher of each game to make them
available for the BC program, they also have to take into account that the original xbox games were made for nvidia and to run them via emulation legally on the newer hardware also require nvidias permissions.

Dead or Alive 3 on the original Xbox.

Dead or Alive 4 on Xbox 360.

That wouldn't make much sense! Microsoft announced they want to keep the 360 alive well beyond the Xbox One's release. They'll keep supporting it for years.

well remember the original Xbox run at the same time as the 360 till the original LIVE was phased out, with MS planning to at least keep the 360 alive till 2015, there will be plenty of time for both to co exist until everyone can move up to a the next version
console

We still have plenty of life in our Xbox One systems. The 360 was alive in my household until about a year ago. The graphics on the newer S versions and X will last longer than the original Ones.