I don't see a problem bumping it every game unless they are very short games, and you are knocking one out every day lol.
I finished KH Chain of Memories and now I am on KH2. I sadly won't finish before KH3 is out, and I have like 3 more games before it. I am fairly patient though, so it isn't a huge issue. The bigger issue is I will be working full time soon, and probably will barely play any games.