Tesla, while one of the truly great electrical engineers of all time, one of the best engineers of any stripe even, was often full of shit. To be blunt.
He made many outrageous claims that perhaps seemed almost within reach to him at the time, but were just science fiction. I've heard this attributed to desperation to attract funding or to vindicate perceived slights or lack of public credit for his real accomplishments but I'm not sure. Perhaps he was just so full of ideas that he felt less limited by what was actually possible. Maybe he was just hooked on proving people wrong? If his reputation with the public, his peers even himself was built on doing the impossible, maybe he was looking for the next impossible thing.
Fascinating guy, but when a man who designed spaceship drives, antigravity, deathrays, intercontinental wireless power transmission and earthquake machines also
looked for the ether, I'm not going to throw a century of observation and solid theory away over it.
edit:
When and how were either of their theories "proven not to exist?" Maybe someone just theorized that they don't exist and you think that is proof?
The ether hypothesis predicted results which were not found and is fundamentally incompatible with relativity which predicts results which are found.