...how long will it be before professional pilots are just like the
men that used to be in an elevator...

I'd put money on 50 years, +- 20. The technology already exists, but
it'll take a long time to make it cost-effective and overhaul the
infrastructure needed to implement & support it.

...(or even out of the cockpit)?

Given that the above comes about "on schedule"; 50-50 we'll see routine
unmanned cargo flights over ocean routes by 2075. Passenger flights;
not for at least a century, probably half again that. We're talking
several rounds of revolutionary advances in computing intelligence and
fault-tolerance to come up with a machine that can safely and
effectively replace a passenger aircraft flight crew at something
approaching the cost & weight of same, plus a LONG run in the
aforementioned cargo aircraft to prove out the tech to where your
average traveler would board RoboPlane. The psychological issue will be
more difficult to overcome than the technological one. Note that a lot
of people don't even like to ride in automated subway cars.

All IMHO, of course, but I'd like to think it's a reasonably
well-informed HO.

RH (PP-ASEL; software engineer; AI maven)