XBOX 360 Back Compat games run like they are on a low spec emulator...

Could not you integrate something like an emulator (as software) into the consoles?

In essence, that is what Microsoft is doing with Xbox One's back-compat feature. The back-compat file includes emulation software to turn Xbox One into a virtual Xbox 360 or original Xbox.

They would have to include architecture from the 360 or emulation to run those games. It's not about specs it's about the extra requirements they would need to allow it to read, recognize, and run those games. To do that will end up costing you more for
the system. Generally speaking the majority of players don't end up using backwards compatibility. In the end it's this simple, it's cheaper not to include it.

For clarification: Original Xbox games on Xbox 360 require an official Xbox 360 Hard Drive be installed in the console. This hard drive contains a hidden partition that includes the emulation files needed to run the Original Xbox game. This requirement
is the same if you're running one of the hundreds of OG Xbox games on disc on Xbox 360 or if you have downloaded them digitally.

On Xbox One, the back-compatibility for OG Xbox is built-in, and the games install in the same manner as Xbox 360 back-compat games (you download it from the Store, or you insert the OG Xbox game disc).

Emulation is the reason. Biggest reason is the change from a Nvidia GPU in the first Xbox to the AMD/ATI in the 360. A lot of graphics routines don't have a similar function on the 360s GPU and have to be run in a different manner meaning it can take several
times the computational load to carry out the same operation with that overhead. Some games work well like Ninja Gaiden or Halo 1&2. The emulation is different for each game with backwards compatibility. Mercenaries works, but there are bugs in the emulation
that make it unplayable after a certain point in the game and it becomes unplayable. If you check the list of backwards compatible games you will notice several have notices of the bugs running on the 360.

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Reason the PS3 systems that had backwards compatibility literally had the PS2 CPU in the system as well since software emulation was too complicated or time consuming.

The game disc just proves you own the game. The reason for the download is how the backward compatibility works.

It works by wrapping a 360 game in an emulator that the Xbox One sees an an Xbox One title, which is why commands like "Xbox, take a screenshot" still work.

Emulation isn't perfect, even for systems going back decades. Microsoft have to tweak their Xbox 360 emulator for each game to ensure that it works as best as it can.