One thing I've always disliked about Pokemon is how tedious and dull some parts of it are. This includes breeding, soft-resetting, etc. for ideal Pokemon. I don't think the game should involve you literally working for your Pokemon. It's simply not enjoyable and I wish there were more methods to get around it. (Destiny Knot and the automatic perfect 3 IVs for legends are nice, though.) Personally, I would rather quickly make a team and get onto the good stuff: battles. Battle simulators let me do just that, but it's a shame the actual game fails in that aspect.
Additionally, I've never liked IVs and natures at all. I want to be able to catch a Pokemon and for that one to be viable right then. It really sucks when one realizes that their in-game team has horrible stats and has no luck in competitive play. I do like how natures provide some uniqueness to each Pokemon, but I don't think they should affect stats.