Is there any particular reason why we can play Xbox 360 games such as mass effect via...

none for me, but the main reason i'm keeping my 360 is so my wife can play Mass Effect... so Mass Effect 1/2/3.

I totally agree with the re-play philosophy. I have 4 saves, each a different named Shepard with a different series of events and particular people alive and dead (with in-game reasons for each). Even if I say I'll only do 20 hours for the other 3 that's
actually 100 of game play just in Mass Effect 3 alone *and* it assumes I won't want to start a 5th play through of Mass Effect 2 just to import a new set of variables in Mass Effect 3 (I replayed Mass Effect 1 once after getting Mass Effect 2 to intentionally
set up a story line).

No, I haven't bought the game. I wanted to buy it as a first try in the Mass Effect world, because Mass Effect Andromeda is upcoming.

It's the first time I hear that reason. But what I did found was:
http://www.polygon.com/2016/11/7/13552118/mass-effect-2-mass-effect-3-backward-compatible-xbox-one

That's why I started searching, but untill now I didn't find a reason why I can't buy Mass Effect 3.

Why would they? It would be perfect marketing. Imagine the press releases at the release of Mass Effect 3.

"The Xbox 360. The only place to play the complete Mass Effect Trilogy."

Now where would you be buying the third and final game if that had been the case?

I like Mass Effect for many reasons. I like Mass Effect 2 for other reasons. Mass Effect 3 is a decent game, but they cut out so much it just didnt feel like a Mass Effect game should. The opening Press Start screen in Mass Effect with Vigil's Theme playing
is probably my favorite moment in gaming history however.