That would wreck the economics of pro cycling because most of the teams are partly sponsored by bike manufactures. Those manufacturers want to be exclusively associated with particular winning teams for marketing purposes.

So what? We have to be afraid of changing stuff because the current statu quo of pro cycling would be affected? That's a pretty weak argument.

Motorsport is sort of similar where manufacturers build cars and there are independent regulations about the cars that define a class. There are spec racing series confined to single cars with very limited additions (safety) that are more oriented towards the driver in terms of competition (spec miata and spec bmw come to mind), but any international world champion type of sport is probably going to require enough monetary backing that manufacturer and aftermarket sponsorship is required to even afford to compete in the first place.

I don't think you understand how pro cycling works. Unlike other pro sports, cycling teams can't really sell tickets to spectators. Most of the revenue comes from sponsors for marketing purposes. So any change that makes it less effective as an advertising channel is a total non-starter.

> make it rotate randomly

In the days when Sussman was a novice, Minsky once came to him as he sat hacking at the PDP-6.

“What are you doing?”, asked Minsky.

“I am training a randomly wired neural net to play Tic-Tac-Toe” Sussman replied.

“Why is the net wired randomly?”, asked Minsky.

“I do not want it to have any preconceptions of how to play”, Sussman said.

Minsky then shut his eyes.

“Why do you close your eyes?”, Sussman asked his teacher.

“So that the room will be empty.”

At that moment, Sussman was enlightened.

(http://www.catb.org/jargon/html/koans.html#id3141241)

Or, in other words, making something random does not make it fair; it is still just as unfair as before, only unpredictably so.

The point is that everyone would be riding identical bikes. The rotation would be to stop the teams optimising around the quirks of a particular bike.