I personally don't like the "With Anyone/Basic Brawl" right now =/ All my reasons basically being the same as The Hypnotist's
What I think Sakurai should've done was make their online like Guitar Hero 3's is with a few extra features.
In Guitar Hero 3, when you're wanting to search for a random match, you start by selecting whether or not you want it to be a ranked match, what type of game mode you want, what difficulty, and the number of songs you want to play. After that, it just sends you to the search screen and you're good to go when you find someone.
In-game, you can see their name, their scores, their entire fret board just as if they were right there in the room next to you.
It's basically just like regular multiplayer, but with the ability to play "with anyone" across the globe.
Brawl could have EASILY done it just like this. Want to search for a "With Anyone" game? Okay, start out by choosing the online option, then have it take you to where you can select the game mode, the stocks/time limit/coin limit/ etc. items on or off, number of players, and whether or not you want it to be ranked or something. Then, in game, allow for you to play the game with the person while being able to see their tag if they decided to put one up or something.
As a game creator, you can set everything up just as you would a normal game, with the exception of maybe something to also set up just how many people you want playing at a time.
What they could add is a "request/add as friend" button at the end of each game, that way if you have a good match with some random person, you can see if they'd be willing to add you so that you could fight again instead of having to just hope to get lucky enough to find and play them again.
Another thing they could add is a "Start Game" button for the game creator. That would easily allow the creator to allow as many players as he/she wanted, whether they want it as a 1-on-1, 3-for-all, 4-for-all, etc.
With all of that, I'd be MUCH more satisfied with it. As of now, it seems the online is only going to be an "Oh, I'm bored, so let's play this" thing instead of the "Hell yes, online time" it should have been.