"Informed helplessness" probably isn't the best frame for the concept, but maybe more like a cost-benefit analysis for giving a shit (CBAGAS), or the Gaullic shrug ( ¯\_(ツ)_/¯ ). My brother and I both lived in DC once upon a time. We both got parking tickets, some of which were legitimate and some of which were made up by the meter maids because the DC government is banking that you'd rather just pay $20 than go through the hassle of an appeal (which they usually just ignore). I would get enraged; my brother would just shrug and say "cost of living in the city--you want to walk home from your favorite bar or to your favorite restaurant, this is what you put up with." It wasn't that he thought it was okay, he just decided it wasn't worth the mental energy to get mad about it.

I still get mad about them, but I can see that his perspective is far preferable.