Maybe a quasi-competitive would work in theory, but it'd be pretty much a massacre of players who want to play this game casually and not really ones who want to get better or try their best.

Either way, you will not eradicate smurfing. There's only ways to help soften the blow of smurfs, and I think this rule change actually made it worse. Not only that you can't queue with your lower (or higher) ranked friends but it also takes the highest MMR. So an LEM can queue with an MGE, but the difference in skill level is massive, and it's still not fair. There's no "fair" way of going about this. The only way you're going to address this smurfing problem is by making it so it's easier for players to queue with their friends, and I feel the old system did it better than the new one, maybe it is fair to put a cap, but a much higher cap on ranks who can queue up together. In addition to that, they should bring back the avg mmr system. Like I said, no system will ever be perfect, but you have to choose a system which will be the most fair.

The more reasons you give players to log into an alt account to smurf, the more common they become. Even in League of Legends where you need to get to level 30 to get into ranked you still see smurfs and while I've not put any time into League in over a year, I did see smurfs fairly frequently. In my honest opinion, to help decrease the frequency of smurfs this is what needs to happen:

-New accounts need to be in a quasi-competitive environment for an extended period of time, such as 20 wins in a quasi-competitive environment with no limit on how many wins or games per day. Existing accounts should be immune to this.
-Allow a much broader queue up system.
-Ensure MMR is averaged out & not the highest MMR.

This will decrease the need/want to smurf, and decrease the population of them, and while not eradicating it, it will help ease the frequency in which you see them.