> The trouble is that people have different preferences for different equipment and by mandating one particular bike, you disadvantage a lot people based on who does better on a particular bike
This is not backed by fact.
Most world tour riders have very little choice on their equipment, nor do they choose the team sponsors. They have some leeway on a few third party components of their choice and can usually which frame model they use among a tiny selection of less than 3 models but that doesn't change drastically how the bike ride really as long as the bike fits. You could totally make a race where everybody ride the same kind of bike, and riders would be able to choose the frame size, saddle, stem and handlebar size, and possibly clipless pedal models that would make everything more standard.
Actually in Japan they do something similar in keiring. All frames are built with steel tubes, they use old styles of pedals with clips, and only parts stamped by NJS, following design and construction principles of track bikes of the late 70's, are approved. Sometimes regular olympic track racers spend a few months in Japan in the off season to get some additional money, they swap their high end carbon bikes prototypes to what looks like vintage track bikes of the 70's, you can actually see the bikes bending under load, yet the best riders with the best strategy of the day still win.
https://invidious.incogniweb.net/watch?v=9GWw31J60cM