I found the same with folders too, I like things to look neat and be apgrouped together but I forget about things once they are in a folder, plus I love the look of some icons. I try to keep everything grouped on screens ie, all my platformers on one screen etc but that always gets messed when I dload new games and they go to the first empty slot nearest the home screen. My ideal ios feature would be the ability to tag apps, then I could just type in say platformer or shooter and have a list of all installed games that match. I am trying to cut back how much I buy but it's difficult with the cheap prices and accessibility of the AppStore. I've been really good and only bought two titles this week, it helps that's it's been a slow release week though lol.
I would absolutely love a tagging system. Setting it up so I can rate games and categorise by genre or any other keyword I can think of eg. Relaxing or Short. That would really help if you could then sort them instantly automatically. I have all my games out of folders when I'm not clearing out but I have them alphabetised. I'd love to have them organised differently but that's a whole other mental issue! Now, if they made a game called App Organiser then I'd play that all day...
Folders work quite well for me. I have one labeled "Playlist" on my homescreen, for games I play now and then, want to get back to, or finish soon. Plus one or two games I actively play directly there. Everything else goes onto the second screen, sorted in folders by genre (e.g. "Gamebooks", or "TBS").