Well, it is just a game and you can't expect much when playing with random players, everyone is going to play the way they think it is better (as they should). If you want to have more well coordinated matches, maybe joining a squad would be a good idea. Plus, Splatoon is a shooter. Even when the focus isn't killing the opponents, it is hard to not feel tempted to shoot them to death.
As for me, I play mostly the Splatoon community's most hated weapon (roller) so I am always covering the clean corners my teammates forget/don't bother painting. And I plan to main the paintbrush if doesn't suck too much, so this is something I will probably do regularly.
And no, voice chat is not needed. In fact, it is a good thing the feature is absent from Splatoon. It would be really annoying to have people bothering you because you forgot to paint some random tiny little spot.