The NFL bans all logos on NFL broadcasts, except the ones it approves, so they can tell a sponsor like Bose that they get an exclusive when they buy advertising (which is what providing those headphones is). They don't want players or others undermining their efforts to sell advertising. There is nothing wrong with that at all. They have gone to a lot of effort to make selling advertising on NFL broadcasts very lucrative and they want to protect it.
This does make sense to me. I can see why Bose and the NFL would want to avoid "free" advertising for someone else in general.
However...if it is equipment without a team logo and is
not related to the game, is it really fair to penalize players? Bose's sponsorship is for head
sets, which, in my mind, covers communications and not necessarily music.
Jerseys? Yes, lock them to a brand for uniformity. Shoes? Yes, lock them to a brand for uniformity. Other apparel? That makes sense, too. NFL and team logos will be on the gear, so it's fair to expect some sort of control over the brand image(s). Music headphones? Those aren't related to the game, and if they aren't branded with NFL/team logos, I don't see a reason why the NFL would ban them at all times (the ban includes practice sessions and in the locker rooms).
And on top of this, players are free to seek their own sponsorships. A ban like this sounds like overreach (since it goes beyond the field), hurting the players' abilities to secure their own sponsorships.
Basically, if the NFL only covered the ban on the field, I could understand and be okay with it. But extending it as far out as they are is wrong, and they might end up getting burned by it.
Side note, I think it's kind of great the Colin Kaepernick got fined for wearing Breast Cancer Awareness headphones. Almost forces the League to send mixed messages, doesn't it?
I don't know that this would extend to the TV announcers. It could, if the contract between the broadcasters and the NFL required it. Since the announcers are not using exclusively Bose, I think it is fair to assume that the NFL's deal with the broadcasters does not cover that.
The NFL is powerful, but TV announcers work for companies that are just as powerful--if not more (CBS, FOX, ESPN, NBC). I doubt the NFL will try to tell those companies what they can and can't use...