Probably a dumb question, but how does it work when riders change wheels in a race? I can imagine that within a team they all use the same kit and the brakes are set up accurately to allow interchange of wheels, but what if you get a wheel from a neutral service car? Or does that just not happen?
Same issue with groupset, rim width (non disc brake), tyre clearance and probably more things?
The idea is probably to keep the rider rolling along until the team car can sort out a replacement bike.
Otherwise the neutral service bikes and cars will just provide tweaks to gears and brakes and the occasional help with putting a chain back on. I think?

Disc shims to set up different wheelsets.
For road teams its one of the gripes with discs, two pot calipers are less of an issue than 4 pots
Neutral Service has long been little more than an excuse to ponce around in nice cars advertising your wares - Mavic did very nicely out of it for years at the Tour for example.
Even in the days of rim brakes and QR, it was a task to get the correct wheel - carbon rim vs alloy, Shimano vs Campag and so on. Now, with the number of wheel variations, it'll be almost impossible - rotor size, cassette range, hub/disc spacing, and so on. Easier to wait for the team car and just have a spare bike handed down.
At amateur level, having Neutral Service has long been completely pointless. Far too many variations with riders on a mix of 10, 11, 12 speed kit, disc brakes, rim brakes... Plus most riders don't have the skills or fitness to get back into the race anyway and there's no convoy to help them.
Surely you can just carry a wedge (flat bladed screwdriver basically) to jam into the caliper to move the pads apart, then pump the brakes to reset them. Another way to do it would be to use slightly thicker rotors on the race wheels and slightly thinner ones on the spares.
I think you're overthinking it. The TSSSK TSSSKK TSKKKKK of a rubbing disk is annoying, but probably less of a drag than we imagine.
And neutral service is just a way to get a few more Shimano/Mavic/Skoda logos in the caravan. Remember the debacle when Froome actually needed to use them? Bikes 4 sizes too small and the wrong pedals, the idea that anyone would ever actually need to use one of the Mavic bikes (actually Cannondale's from circa 2003 IIRC) never occurred to anyone.
Or take 2 seconds to loosen the post/flat mount, squeeze brake and tighten in new aligned position?
Wait, let me guess, that doesn't work for flat mount?
And to add to what crazy-legs said there are also at least three different pedal standards (spd-sl, look, speed play). Didn't Froome have to use a Mavic bike briefly and his shoes weren't compatible. Often you see riders borrowing a bike from a lesser teammate until the team car can get to them
Differing gears a bit of an issue but with pretty much everyone on 12 speed now it's a bit better. Easy enough to have Shimano and sram wheel on car, might not shift perfectly but better than waiting depending on where your team car is.
In the pro tour there's only really two drive trains: SRAM 12 speed and Shimano 12 speed. Then maybe disc + rim, so 4 rear wheels and one front wheel model to carry.
In the pro tour there’s only really two drive trains: SRAM 12 speed and Shimano 12 speed. Then maybe disc + rim, so 4 rear wheels and one front wheel model to carry.
There's still one WorldTour team runnning campag: https://www.bikeradar.com/features/pro-bike/worldtour-bikes/ (I was surprised there aren't more).
I dont think anyone uses rim brakes any more, do they? (UAE and Ineos held out for a while but pretty sure they're all disc).