I played online on the Wii quite a lot, it was fine. Smash bros a ton, 007 Golden Eye and The Conduit, and good old MH Tri.
Literally a thousand hours in that last one alone most of which was spend online. Did you not use Ethernet? Wi-Fi was shitty for sure, because everybody had shitty wi-fi back then. (I’m also not saying it was amazing, but it was free and serviceable)