Kylo should definitely inherit Vader’s lightsaber when he completes his training.
Yes, because one lightsaber miraculously retrieved from oblivion wasn’t coincidental enough …
Really any type of logic regarding things/people surviving falls was thrown out of the window in ESB. Luke surviving his fall is something we attribute that to the will of the force. The same can be applied to a lightsaber.
Of course, hardly anybody complained when Timothy Zahn did the same thing in the Thrawn trilogy. But put the same idea in a film and you have Internet forums exploding with nerd rage.
I think you’re asking for consistency in the Star Wars community. I think you’re asking for too much.