Mario 2 was never a 2-player game like that... I agree that it doesn't get enough love though. I consider SMB3 and World to be better, but 2 is still a solid game.
It was the first game to give Peach a broader role than just being a damsel in distress. It gave Luigi his own identity, just like the OP mentioned.
SMB2 blessed us with Bob-ombs, Shy-Guys, and Snifits, which are all Mario series staples.
The villains really don't get enough attention either. Birdo shows up every now and again, but Mouser, Triclyde, Fryguy, Clawgrip and Wart don't get enough love.
The boss battles were a massive step up from the OG game.
This really shows how Super Mario All-Stars was one of the GOAT gaming compilations. TAll-stars messed up the brick physics in the first game, but the SMB2 and 3 remakes >>>>>>>>
There should have been a SMB2 mode in Mario Maker. Dope game.
EDIT: Toad and Luigi are the best characters for speedrunning. Toad was the fastest (especially when holding an item), while Luigi's crazy jumps break the game in all kinds of ways. Peach is cool but she was clearly the easy-mode character for beginners. As for Mario...
....well, I like Mario.