I remember going down that path when I was an undergraduate. Fortunately I had a very experienced theorist to hand who explained that, yes, people did try that,

I remember going down that path when I was an undergraduate. Fortunately I had a very experienced theorist to hand who explained that, yes, people did try that, but stopped bothering because it doesn't generalize to general relativity, and there was no point keeping two mathematical toolboxes around when you could have one.