I doubt that Scott will reply to this, 5 years later and on a different site, so let me try instead.

there are only three objects you can write in terms of the metric tensor which transform the “right” way (G, T, and g itself).

Hindsight bias? There are plenty of such objects. Google f(R) gravity, for example. There are also many different contractions of powers of products of R, T and G that fit. There is also torsion, and probably other things (supergravity and string theory tend to add a few).

You might want to argue that G=T is "the simplest", but it is anything but, for the reasons Scott explained. Once you find something that works, you call it G and T, write G=T and call it "simple". That's what Einstein did, since his first attempt, R=T, did not work out.