Unfortunately it's not just well within their rights, it's their legal obligation. The stupid situation that is America means that for them to be able to maintain their claim of ownership on the IP trademark, they have to both actively use the trademark and actively police unauthorized use of the trademark by others. If they don't, they risk losing the right to claim the trademark, which wouldn't just mean independents running servers for the game, but also would mean unscrupulous entities could produce and sell merchandise featuring the trademark en masse without having to seek permission from or pay any commissions to Valve.

It's shitty, but it's more shitty because of the stupid system we've built than because of any intentional malevolence on Valve's part, imo.

Important caveat: I am not a legal professional and it is entirely possible my understanding of trademark law is flawed, but this is my earnest understanding of the situation.