FAF has a problem with how modded games are treated
It's not a problem. It's different opinions that lead to on/off checkbox. There is no problem with having different preferences to how play the game.
FAF doesn't have a huge number of games or players
So we shouldn't make it worse by forcing the players who don't want to play mods to use black magic to determine which mods are on. Especially when there are multiple of them.
People's choice of whether to join a modded game or not isn't impacted (since the client would still show what mods are active)
It's not. Client UI is buggy and the only way to do it for sure is use the filter. It's the case with many survival maps when you're using list game settings in client. The only hint to figure out is looking for "survival" keyword, but there is no guarantee that a modded game will game one.
Maybe you're using tiles instead of table lobby listing? Then it's easier to determine mods. But I would not like to be forced to using tiles just because I don't like (most of the) mods (most of the time).
they would lead to less community fragmentation
The goal you are trying to achieve is exactly community fragmentation. If the more modded games will be hosted, the same amount of players will be sprayed among them. For the same reason why if 33% games were FAF, 33% games were FAF Develop and 33% games were FAF beta balance it would spread the small pool of players in a bunch of semi-empty lobbies that will take hours to fill.
Community fragmentation is not pure evil per se. Matchmaking & custom are also splitting the lobby in half while playing only astrocrater approarch doesn't split anything at all. But it's foolish to propose exactly what will create more of splitting as something that will make create less of it.