Is not that Tamaki wanted to be the vocal, she wanted more to just be in the band together.
And I think it would be much harder for Tamaki to just go talk to Kaho and say that she should be the vocal when every time she reacted very badly about the possibility.
Plus, they're both beginners, just as Tamaki improved on the guitar Kaho could improve on the vocals.
In the end both had their own problems, Tamaki was able to overcome it while Kaho didn't and made things worse for herself. Their personalities are somewhat the opposite, aren't they not? While Kaho ran away not only from the club but from the whole school, Tamaki ran in the opposite direction. And when I think about this I feel that maybe it's understable that Chiriho admires Tamaki so much, and for Tamaki to share that admiration. Chihiro is also confronting all her weakness head on, criticism and push back from other gives her energy to fight back.
Chihiro x Tamaki, that would be an ideal ship.
(Chihiro is partly following Tamaki's steps, with the acceptance of he voice and effort to master the guitar)