I think that one of the things I really want to see are tabbed lobbies. Only being able to be in one lobby at once is a massive limitation and generally poor design. The simple fact is that I'm usually OK to play a few different games and game types and would be happy to launch with whichever of them fills first.
If you have 5 lobbies open that implies there are 4 of them you are not going to play in but still take up slots in. No.
What might have the same effect is if you opt to launch with some set conditions (that are variable, like 2-4 players, multiple game types), and enter a queue that that matches you up with players based on your conditions. This will put you into a single lobby, or if someone drops out, replaces that player with you. Thus, the lobby stays full and you don't have to wait for players to fill, but you still get the 'choice' that you outlined. Well, to a degree anyway.
That no longer matters. Since everybody who wants to can now join the lobby, having someone drop out of it isn't going to be a big deal, since there's going to be far more people joining lobbies- and if you don't feel like sticking around and waiting for your exact preference to launch, then just join multiple lobbies yourself. You no longer have an investment in waiting for a specific lobby to launch. You have slots that aren't full anyway, else the lobby would have already launched, so what does it matter? The only potential loser here is PA's server infrastructure, who would have to cope with a fair chunk more traffic in the lobby system.
What you are proposing is going to make starting a game nigh impossible due to a constant stalemate of people dropping in or out. The same 5 people could all take up many lobbies waiting for each other with no one lobby ever getting anywhere or they could all pick one lobby and start playing right away.
You don't get a higher number of players with this, therefore you won't get quicker gamestarts. All you get is a higher frequency of people dropping in and out which leads to it being way harder to find a full game.
There is actually a use case for this: people that just want to spectate. I do this occasionally in Spring when I just want something to watch next to my movie, but it always takes longer than I'd like because I'm locked into waiting for a single game instead of being able to pick up the first game that starts. While we're on the topic of joining lobbies, by the way, there should be a special "join as spectator" option for when you want to spectate a game that's already full. The simplest solution would be that you can join multiple lobbies as a spectator, but only join one as a player. Even better, you could actually spectate another game while you're waiting for the game you want to play in; as soon as the main game kicks off you leave the game you're spectating and start up the game you're playing in.
I suspect that spectating will be even less needing of something like this in PA, given the replay system Uber have I'm fairly confident that if there is live spectating you will be able to jump in and spectate games that have already started so instead of waiting at all you just join a game that recently started instead.