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I guess this isn't really a gameplay feature that bothers most people, but here goes...
Gens 5 & 6: forcing you to beat two or more powerful trainers in a row after catching your title legendary, with zero options to save before the battles. This made getting a correct-nature Yveltal and Reshiram so fucking difficult for me that I gave up. Especially considering that my team was underleveled when I fought N and Ghetsis so it was a miracle I beat them in the first place. Going through the whole ordeal again just to make sure my Reshiram was Timid, or making sure my Yveltal was modest after beating Lysandre just seemed like less fun to me than watching paint dry.
Also, forcing Reshiram into the front of my party is a dick move to players who prefer to keep their box legends untouched. It forced me to let Reshiram die in order to prevent exp. gain. At least gen 6 fixed that tidbit by making Yveltal an optional party-member.