I don't think this is remotely true. I just checked Delta and British Airways; both show the aircraft type in "details". (Pick the 747 flights from BA while you still can!)
> even if they do, they seem allowed to change it at the last minute
Airlines shuffle aircraft occasionally, but usually the aircraft type for a particular flight is predictable. If airline A flies the 737 Max and airline B flies the A320 on the same route, people will flock to airline B.