They tried, sort of, a long time ago, kind of? XNA Game Studio (which still lives on independently via
MonoGame) was a low-level entry from Microsoft designed for independent game development to publish on Xbox 360 and Windows Phone and other platforms of the time. It as mostly used for 2D or small-scale games like Bastion, The Dishwasher, & Weapon of Choice, but it could do 3D (and had XBLA Avatar integration) or whatever you could build out of it.
* I also sort of recall there was some pro version of the XNA tools or something else at the time MS was also experimenting with for more advanced game development on Microsoft tools. (Anybody else remember like a 3D demo of a lady in black-and-white with red lipstick drinking tea? What was that demo for?)
Ultimately, by the time of Xbox One,
MS's messaging about engine licensing by the time of its ID@Xbox program was that there was already plenty of good solutions on the market already.