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I think that in situations where there are a small number of elevators this is still true to a certain extent, but more and more, any situation in which there are more than 3 or 4 elevators in the core, is likely to have a traffic control computer coordinating all of the elevators.

After all, how else can they all be on the wrong floor, going in the wrong direction, when you need one?

As amazing as this seems, it is entirely feasible to have elevators with absolutely no computer hardware or software involved: most elevators you use have zero computer hardware involved, in fact. It is very simple (comparatively speaking) to build decent elevators that are very reliable with zero computer stuff, as there's many ways it can be done with simpler electromechanical hardware.

Most modern elevators use microcontrollers, we had some old ones at work who were relais based (open rack with clicking things alover) quite relyable. but they don't live forever...
Modern ones include things like automatic leveling, smoother rides and in larger buildings some clever behaviour of the elevators can be usefull.
Using Microcontrollers with a couple of input, outputs
and a program saves a lot of additional wires and relais.

I can't imagine an elavator in a large building that didn't use a microcontroller or PLC.

How do you get your electromechanically controlled elevator to look at 10 requests from 10 different floors for up or down direction and schedule them appropriately with hardwired relays?

I'm sure it's possible with lots and lots of boolean simplification and cabinets full of hundreds of relays, but each relay is a mechanical failure point, and the project would be ridiculously expensive. I can buy 3 or 4 relays for the same price as a cheap PLC that can emulate thousands of relays.

Certainly PLC's are used, and certainly there's a microcontroller in them: but they're also certainly not running anything more than a very simple embedded bit of software in a very tight loop.

Yes, PLC's simplify things immensely, and can often make things much cheaper once things start getting complicated and allow things to be reprogrammed as needed, but they don't require even anything as complicated as QNX, or as much RAM: they've been around and used before QNX was around, in such places as car factories. PLC's have a minimum amount of memory, only as much as is required to hold the current state of all the I/O hardware and the limited number of timers and such, because they don't need anymore than that.

Put in the original context of "I wouldn't use an elevator with anything else" even with the more sophisticated elevators (how many use QNX?) causes options to be extremely limited.

FYI, yes, I've programmed PLC's in industry.