Honestly, I don't know why Turkey was ever allowed into the NATO Alliance. I can only speculate it was because they had nuclear weapons and NATO wanted to have some influence over them?
Turkey has pretty much always been a wild card in the region.
Turkey was a fairly benign socialist state like many Muslim countries at the time. They also happened to occupy a strip of land where we could conveniently place nuclear missiles rather than shoot them around the world (think Cuba).
You're absolutely right, though. NATO should have stricter standards for membership and this problem definitely brings that issue to the forefront.
Rather than let this fracture NATO, we could potentially let it reinvigorate NATO with a purpose. I think Turkey is currently getting a pass because it isn't a Western country, but that could change very fast.
Putin knows this too. I think he also knows that he won't get everything he wants, but hey! Nothing ventured, nothing gained.