I agree that hand written letters don't scale. I also agree that a hand written letter could elicit positive perceptions of the company.
I'd say the reason to do something that doesn't scale is that the rewards for doing it don't scale either. Sitting face to face with a user makes sense when it provides better feedback than A/B UI tests on the homepage. A phone call makes sense because when it opens a dialog that is difficult to approximate via bulk email.
My gut says that a hand written letter probably creates a higher threshold for bi-directional communication: the friction in the channel that makes a hand written letter standout makes it socially difficult for the customer to respond in a less "romantic" channel...I mean, an email response to a hand written letter feels a bit tacky...
...at least with someone I don't know well. Which leads me to think that a hand written letter might be the sort of non-scaling thing appropriate when a company is large and the relationship with the user is non-trivial.
Finally, I know that if I was thinking it was a good idea it would probably be because I'd rather write a letter than make a phone call or in person appearance. That's just my personality favoring something psychologically more comfortable than the risk of rejection.
Good luck.