I don't really see type advantage as an issue in the anime because of how often it gets dumped on
And getting KO'd really should matter. It means you are not good enough. For instance, against Gary, Charizard knocked out 3 and was undefeated. Snorlax only knocked out 2, and was defeated. That just makes things obvious.
--
http://img.imgcake.com/Xiiijpgen.jpg - Me, as drawn by Ayvuir (who is also a giant douche)