It's done at some airports, small ones where they share gates, where contractors run the check in counters, and the kiosk has a bunch of logos and you touch the one for the airline you are flying to get started.
I've never however seen them all using the same computers, it's always been if you need xyz airline and they are at the abc terminal, they move over to the next terminal.
Interesting concept to roll up to a large grown up airport. I would be a bit shocked if the airlines would go for it.