American banks do not rank well on a global basis for neither solvency or safety. The new buzz word to digest is Bail-in. Do a quick internet search or watch any one of dozens of videos on the subject. If you're pants are still dry you've got bigger stones than me, are abjectly stupid or are drinking from the koolaid....
Essentially, us common folk with some cash to deposit will be used to rescue banks when next they crash - instead of a bail-out you will lose some of your deposit as it's converted to equity to save the bank. You get negative real interest returns and if that slight wasn't bad enough you get to rescue the bank. The fat cats that made millions in quarterly bonuses ride off into the sunset and the sheep will be left holding the bag. The FDIC is not your insurer, instead they will be the bankruptcy executor that bends you over, shakes out your pockets and fucks you.
Everything you've been "taught" about the FDIC is at beat a lie. Keep excess cash in money market accounts at brokerages, with smaller banks less likely to play in derivatives and/or credit unions (they actually are for the benefit of their customers - big banks see you as suckers to be swindled and sucked dry).