To people who are gifting the president because he/she is the president: A pre-printed note or a note written by an aid is fine.
To people who are gifting the president because they happen to have a personal relationship with the president: A pre-printed note would be just as rude as it would be for anybody else. Which is to say that if you have a problem with Joe Schmo sending a pre-printed note to his great aunt Sue to thank her for the wedding gift, then you should also have a problem with the president sending a pre-printed note to his/her great aunt Sue.
Becoming president (or a doctor, or a lawyer, or a billionaire in charge of running a company that millions depend on, or just a busy person) doesn't excuse you from social niceties. However, being someone who gets lots of "personal" correspondence from complete strangers does allow you to treat that "personal" correspondence differently (more business like - hence the acceptability of form letters) than true personal correspondence from people you actually have a relationship with.