I personally think the handwritten note is ridiculous - a waste of paper and time and somewhat creepy. I positively, but mildly, don't like getting them.
I certainly expect to be treated well by the airline to which I give my business, and treated well throughout the extended transaction. And, with my status on BA and UA, I expect to be treated like a frequent flyer rather than a leisure flyer. And there's the rub: the UA FA who handed my one of those notes the other day (and I do accept it might be culturally acceptable in the US whereas it would be culturally unacceptable in the UK) may make the effort, but the overall experience counts for more and, in that case, was let down by rude security in UA's terminal in SF and a horrible United Club experience. Those matter, not the note.