Arrogance is certainly a trait of UA's (and perhaps the US3's) FA's, I have it on nearly every flight, it's why I don't fly UA international anymore because there are so many better airlines with better products and attitudes that deserve and earn the money. From the roll-eyes when asking for a glass of water mid flight or whole can of soda on a trans con, to standing in line near the galley for the slim-line lav and seemingly encroaching on their 'people magazine reading space'. In the domestic market, there is little choice due to regulators allowing all of the anti-competitive mergers.
I've been humiliated a couple of times by UA FA's. The worst was when I was dressed down by a FA when boarding a flight. I was carrying my laptop bag behind me on my back per normal and she insisted I was going to 'hit' someone with it. I've never done that before, attested to that. She loudly insisted I carry it by hand in front of the whole plane so I wasn't rude to the other pax. She didn't do that to any other pax that boarded with similar bags. Plus I was in BG 1 so there were very few in the aisle at the time in the way per se. She just wanted to make a scene.
Point is UA doesn't seek out or train out the bad CS behavior, they just care about getting the plan out on time, staff showing up on time, and controlling costs. IMO the letter might get you some miles or a voucher but that's it.