This is true.
There are other factors, too. Stories come out and there are sponsors involved. Money matters. If you bully people and are seen as a dick (especially if you aren't getting wins), your players can cause stink and then Coca-Cola isn't going to want to give you all this money to have a bad image tied to them.
It was probably always the case to an extent, but with the media having such larger access and twitter being instant, it's exacerbated.
Good point about the sponsors playing a role as well. I hadn't thought about that but I bet you are right.
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