When it comes to NON-Pro, NON-UCI, it can matter quite a bit more. There are some bikes that fit the course better than others. The hilly bike, gravel, aero bike etc. Differences here matter.
In the USA you can race a rim braked bike 2-3# less weight than a disc braked bike. Or do other things to get that bike 4# below the UCI limit.
I think the UCI pros pretty much have similar stuff and the budget to have the bike fit the event.