The amount of precession in Mercury's orbit couldn't be accounted for with known theories of the time.
> he did not carefully study existing evidence and realize it supported General Relativity.
Considering it took nearly 10 years to develop GR, I'm not sure he could have even considered whether evidence supported it or not; it was clear that there was a gap in understanding at the time, as experiments started to show it. Einstein suspected rightly[1] that unifying gravitation and acceleration with special relativity would give a complete theory of everything.
[1] He was only half right; it doesn't explain quantum mechanics. He was a strong opponent of (some parts of QM) for a long time.
> rationality can be superior to empiricism
But it clearly isn't, as we haven't come up with a complete model that explains everything we can observe yet.
That objection is utter nonsense and an affront to reasonable discussion. Empiricism hasn't come up with a Grand Unified Theory of Everything yet either, so rationality's failure to do so doesn't constitute evidence either way regarding their relative value.
Famously, when asked what his response would be if a certain piece of evidence turned out to be against relativity, Einstein replied that he'd feel sorry for who obtained the evidence, because Relativity was certainly right. And much later it transpired that the evidence matched the theory merely by coincidence; that the experiment was flawed. So Einstein nearly had to face that fight. Anyone following the position laid out in your comment would have been on the wrong side of that debate.
This demonstrates perfectly that rationality can be superior to empiricism because it is not subject to the same flaws and contingencies as the gathering of empirical evidence.