If we start with the assumption that a sincere, personalized thanks will be given; the next step is then what medium/formality level is appropriate to the specific situation? I feel like this is the part where a lot of people get confused, or become nervous about doing it "wrong," or (less charitably) decide it's okay to follow their own convenience above all.
We talk a lot about how society is becoming more diverse, you can't count on everyone around you having been taught the same rules of etiquette, and even the most long-standing of rules are starting to change. And people differ on what they find meaningful--for some, a written note is most meaningful, for others they would toss it out right away and would rather hear your voice on the phone. So it's no wonder that people aren't sure what to do sometimes, because sometimes there isn't really a "right" answer anymore.
I think, when in doubt, a sincere, personalized, written-on-paper TY note is never wrong. If I were questioning whether it's necessary to go "that far," I think I would ask myself, why don't I want to send one? And then evaluate whether I really thought the answer was a good one.
Answers like, "It's boring" or "It will take too long" are not, I think, good answers; they're placing my own convenience over showing gratitude to people who did something nice for me. Same with answers that blame part of the process--like, "I have bad handwriting" (type it!) or "I don't know all the addresses" (ask someone!).
An answer like, "I felt I gave a sincere, personalized thanks in person already," "I think Aunt Betty would appreciate a call of thanks more, because she can't see very well anymore," or "My social circle communicates primarily by email for all occasions, even wedding invitations are sent that way," are definitely better, IMO.