They are absolutely possible technology and could be constructed in such a way as to be viable.

Cooling in spaces a massive pain in the arse but if you do it at large enough of a scale it actually becomes efficient.

The problem is we need access to a space elevator before we could build at that scale otherwise you'd be sending up hundreds of rockets just to build data center 20% the size of anything we could construct on Earth. Which would obviously be pointless.

So Elon Musk should be working on a space elevator. Except he can't because that would involve advanced physics and material engineering, both of which he is crap at, given the fact that he tried to make a car out of pig iron.