There is a thing in Starcraft Brood War when players hide their identity so that the opponent does not know what to expect. I wouldn't mind having it in FAF, but mostly to get less stress, as anonymity in fights means there will be no consequences no matter what happens in the game.
Ladder should definitely be anonymous.
Maybe it would be okay to allow for 1 practice ladder game a day where you don't lose rating.
I like this idea more the more I think about it. Anyone afraid of the ladder button can get 1 free game a day to get used to pressing it and get used to playing ladder. It would work for high rated players that have been inactive as well. They can play some free warm-up games that contribute to overall ladder activity. It could also encourage more interesting and risky strategies in the risk-free game for the normal active players. If you can get people into the habit of playing 1 ladder a game a day they are likely to continue and become active ladder players. Some other type of incentive to play 1 or more games per day/week would also help to build this habit.
Of course the big downside is that it breaks the integrity of the rating system, but it is not really any worse than people playing unranked custom 1v1 games, which is the current situation for many high rated players. The integrity of the system is also irrelevant if ladder is dead, which it pretty much is currently.