Oh you know, people that actually wanted people to stick around.

Ok, well as pretty much everyone knows the game is better the more players it has, I'm sure there are actually very few people who don't want  more players to stick around. I can say with certainty every Las Vegas Don has that view, which would mean "the people" should be happy joining them.

But, as you said that not everyone wants to join the existing crews, I am guessing there are further specific criterion to be met, in which case, who are we talking about?

This all seems to be a bit of a mountain made from a mole hill really. 

I've been a CL many times in past, long before rebuild mode was a thing, and I would always tell my sponsors to actively recruit even where we had no space, simply to try and recruit people to other crews in the District/City.

Being instructed to keep your sponsor toggle on is no different than the above, it alerts the family that there is someone looking for a crew, we can then easily inform the recruiting familys of that and the name.