In my experience, you tend to see mostly those of the broad category and some of the general. You almost never see any of the others. I'm curious if that's because people just have no interest in such games or because someone has just not come out and made on(or at least not made on in some time).
First, there's a current X-men+ game that's been around at least a year, as well as a new alt-universe game, so 'almost never' seems extreme.
Otherwise, there's a couple things being discussed here. Some of it is very general. 'Big and sandboxy' vs 'small and focused' is not comic specific, but rather one of our oldest topics. Insert the usual debates on total RP vs. getting lost in the crowd, or on whether logins are actually a measure of game quality or success. And 'include every IP' vs 'just X-Men' is definitely a subset of this.
But FCs do add some particular dynamics.
The slope on FC popularity is pretty damn steep, with a quick fall-off from the top characters. So, unlike with other big game vs. small game stuff, there's essentially an absolute cap based on how much IP you provide. You really can't make the choice to have a 'big' X-Men game. And the harsh cut-off really impacts style preference, too. Being a Gotham fan may be kind of pointless when there's so few key characters and your chance of ever landing your favorite might well be zero unless you help build the game.
This doesn't only apply to people wanting to take the characters, but also to people wanting to play with the characters. Vibe is simply not going to attract RP the same way as Wonder Woman.
And there's a tendency of staff not to be realistic about any of this stuff: no one wants to admit 'yeah, all the good characters are taken, no reason for you to really play here.' nor admit that a given character is just not very popular (or heck, kind of a joke) and probably won't get any RP unless the player is in the top 1% of proactivity and charisma. I feel like there's even a bit of that vibe in this thread already, in the 'why should power level matter?' refrain. It seems to make unrealistic assumptions about every player being cooperative, giving, self-aware, willing to write to others and generally share the spotlight. This are great ideals but... yeah. My experience is that a lot of the players of high powered characters are typically absolutely awful at this. Some outright are in it for the power trip, others are just blithely unaware (ie, I've seen people give the Superman 'World of Cardboard' speech/quote as an OOC context on multiple occasions on these games, offered as proof they were a 'good' Superman player and knew what was up. Except the context of the speech is literally the ultimate 'Lol I was just holding back, I am a living I Win Button', given before Superman solos Darkseid. It's 100% inappropriate in a MUSH context.).
So, IDK. My preference is not to play on a style of game. My preference is to play a character I want to play, and get recognizable comic-y RP. Any game that serves that goal is acceptable, but many games will fail at it.