As it stands I don't believe that regular events would perform that well for clans.
Clan league, literally the biggest clan event of every year got 17 entrants. We have been tossing around ideas about implementing some form of automatic clan competitions run in-game, but we're still settling on some details, and also whether it's even feasible in the first place.

I think part of the issue is in-game exposure, the forums are a surprisingly small part of clans these days now that people use in-game (obviously to play the game) and discord.
Don't want to reveal too much obviously, but please note that we do want to do things that engage clans more in-game, particularly the newer guys that still have the energy to get involved with these kinds of things.
Point is, I guess, we share the sentiment and there are ongoing discussions a out the best way to do something about it.

As for the second point, there is a recruitment board for unofficial clans where they can try and recruit people without worrying about official clans. (Only dying official clans can post threads there; see rules thread in clan discussion)

Part of the perks of being official in that regard are that you're already established and can end up being a bit more visible on the forums, to diminish that detracts from one of the few things that being official actually helps with, and I'd be very hesitant to alter that.

Ty for the suggestion, we always like hearing ideas!

Edit: the term "boosting" gave me a though though. Clans could gain double do or something for games played in their clan server, or could gain xp from matches played in their server even if it's not by people in their clan. I dunno, just spit balling a thing that might nudge people to reply and get a good public discussion going idk