I can't comment on the 360 revolutionizing online, as I still don't do it (finally got a choice other than satellite internet last November with T-mobile, sadly when my grandmother, whom I was caring for with my mother, passed away).
But what I CAN say is that my Wii (and the 2nd I bought used when the fan died on the 1st after 8 years of use) and the WiiU's backwards compatibility got a TON of use, one of my 4 most played consoles to date, with NES, PS1 and PS2 and their gigantic collections (PS3 turned out okay, but nowhere near the 1st two, and don't bother with the PS4, got 10 games for it but have barely but 10 hours total into the console itself since I got it Xmas 2019).
Do I think Nintendo could have done better with it? Yes, but considering the successes with it they had, they still accomplished a LOT with that console after their stumbles with the N64 and Gamecube. I had enormous amounts of fun (and awesome gametime) on that console, and as a local multiplayer console, no other gaming console comes close, not even switch. To date despite Twilight Princess being my favorite Zelda, I won't play any version but the Wii because of the controls, and Metroid Prime Trilogy with the Wiimote is absolute bliss, and despite the few disagreeable changes they made in MP3, many things in the game work so damned well I can only call it "buttery smoothness" because it flows so seamlessly. I'll have to do a count, but I think I have about 50 Wii games (not including digital purchases), 5th most in my game collection behind PC, NES, PS1 and PS2.