The browsers don't have any contract with Alegeus, nor any relationship at all. They owe Alegeus nothing. They're not covered in the TRO. I doubt the TRO could legally be extended
to cover them.
Browsers do have a relationship with their users, who may very well be relying on them to enforce the CA/BF validity rules, or if they can't do that to provide equivalent security guarantees. And in particular many of the users rely on their browsers to protect them by blocking suspicious domains in various ways. So blocking the domains wouldn't be arbitrary, capricious, discriminatory, or anything like that.
Judges don't have infinite sua sponte powers to order just anybody to do just anything. Although I admit they sometimes act as though they did, especially when they feel like their authoriteh has been disrespecked.
Anyway the browsers aren't gonna do it. There's zero chance. So legalities don't really arise. I'm just saying it wouldn't be unreasonable.