He went on with the others for the adventure in the other worlds and I'm fine with that. Kuuga no Seikai was also a great 2 parter aswell. I don't think the character himself needed to do anymore in the series.
I don't think that's really acceptable. Really, Kuuga did more in the later worlds, which had larger number of Riders around than in the earlier worlds. He was just plainly badly used at time.
Not transforming in Ryuuki was acceptable. I thought he was excellent in the Blade World... until the final battle, when he didn't transform and was just knocked out. Then, he did nothing in the Faiz World, played around as G3 in the Agito World and, when he did transform in the Den-O world, it was just for a joke scene. Then, he went back to not mattering in Kabuto...
And he only got to transform again in Hibiki World, just to be beaten up. Really, his participation in the Hibiki World wasn't bad. There was a very large cast around, and he still got to transform and fight. The problem is that it followed many other episodes where he did nothing.
Then, he goes back to doing nothing in the Inoue episodes... Afterwards, he gets to transform again in the final few worlds and the 2 movies, even though they always had Diend and Riders (or Sentai) of each world and some actual general plot going on at times in addition to all that. There's no excuse for his misuse in the first few arcs of the show. He could have fought more without making it his own series.
And when he does henshin, he gets beaten up like Chris Tucker in all the Rush Hour movies.
He was beaten up by himself only once, in the Hibiki World. The other times, like Kiva and Rider War, everyone else was beaten up too, so it's not like he performed particularly bad in those battles.