Most servers are powered by software under Apache and MIT licenses; companies pick what they want and mostly don't give back. The dominant operating system on personal devices is Android, which is free but nevertheless deeply tied with a corporation's interests and developed in secrecy using the same principles as proprietary software.
What would FSF gain by supporting that kind of software freedom, other than a reputation as nice guys? That model of freedom has already won, and from FSF's point of view, it's not much better than traditional closed software.
If the FSF compromises in order to be diplomatic, they'll have to compromise on the only thing they are adamant about: that software must be libre (and there's no such thing as "mostly libre" software). This would invalidate the FSF's mission, which is ideological and their only raison d'etre.
Open source software would probably not disappear, since it's largely successful (and extremely convenient even for companies who don't give anything back), but maybe libre software would. The FSF's concern is libre software, not open source software. I'd like libre software (as well as user rights and our freedom to tinker) to continue to exist and therefore I support the FSF's mission and their principled stance. I'm not as uncompromising as they are, but then again, my job is not advocacy.
I hate to sound paranoid, but I think libre software, user rights and the open internet are under attack, and we need to organize and defend those rights. This is an ideological issue orthogonal to any technical merit of open or closed source software. I'm glad the FSF exists as one of the groups on the side of users.