Because
a) I like challenge in my games (as long as it is fair challenge, and not just "let's make the game impossible just because we can").
b) The idea that I would lower difficulty for the harder parts doesn't really feel different from just enabling cheats to get over the hard parts. Sure that works and I've done that too (e.g. in one mission of the Tie Fighter expansions), but at that point I start thinking what is the point of playing the game anymore, instead of e.g. watching a Youtube-video of someone else playing it.
c) I am not even sure if the game allowed changing difficulty midway, or if it would have meant having to replay the game from the start all over again on the lower difficulty setting.
As I keep saying, I like games where there are no difficulty settings, but only one. Games like Magic Carpet and Dungeon Keeper, for instance. Then I can rest assured that the developer has properly tested the gameplay (so that they haven't just added a difficulty level that is practically impossible), and also thought how the game could be completed by people of different skills. For instance in Dungeon Keeper, the obvious way would be to use more time to train your minions, if you feel insecure, and in Magic Carpet you just need to play more carefully, advancing more slowly instead of flying in the middle of flock of dragons. Plus, Magic Carpet had the benefit that usually the hardest part of a mission was near the start when you had no castle etc., and the longer you survived in a mission, the easier it usually became.
Then I can also rest assured that if I find the game too hard, then it really is about my lack of gaming skills (or perseverance), rather than the developers just being pee-heads and not properly designing and playtesting their game.
I am generally against the idea that I should somehow try to pick the "right" difficulty level. How the heck do I know beforehand if "hard" means a cakewalk or impossible to finish (for anyone)? I e.g. recently finished Deus Ex in the hardest ("Realistic") difficulty, and I never got stuck in the game and it progressed all the time. I would even say it was a pretty easy game in the "Realistic" difficulty, partly because it gave you lots of options, even avoiding encounters.