Genuine question - if you know the recipient got the gift (as it was on a gift table, or because you've seen on the Royal Mail website that it was delivered) what is it that you need from the recipient?
I know it's traditional to write thank you notes, but it is clear from here that that tradition is dying out. I don't send them - I thank someone if they hand me a present, or phone/text them to say thank you if something arrives in the post. I don't let presents go unacknowledged, but nor do I write letters of thanks. As often as not I thank them in person when I next see them, and that arrangement is all I would expect for others. I rarely buy presents for people I don't see very often.
I particularly wouldn't write to someone to say the cup and saucer was broken. Would anyone do that? I would always say that presents were just what I wanted (regardless of the truth) and wouldn't mention it if they didn't fit, or were in other ways unsuitable. So I don't understand the OP thinking along those lines.
People often say that they stop sending presents - even to their own grandchildren or other family - if they aren't properly thanked. I find that very strange, as I give from a motive of wanting to give to people I care about. No strings attached.
Yes, it's lovely if they have time to take a photo of their baby in something I've knitted, or of the recipient drinking out of a cup I'd given them, but life is busy (particularly for new parents) and I understand that. I really don't expect it, so would like to know what it is that people really want.
Is it to see that traditions have been continued? To feel good about themselves for having given a gift? Is that the quid pro quo?
Do people really want to know if the recipient hated the dinosaur jumper they were given and how they would never wear it in public, or do they just want to hear about how kind they are, and how lovely the present was?
I'm with MissA on this one. I'd rather not bother with any of it if it comes with strings. I am a polite person, and was brought up to say please and thank you, but am bewildered by the neediness I sometimes see as regards formal thanks for things, and also as regards people 'not bothering with' sending cards. I don't want people to be 'a bother' to people, and appreciate that times change and life gets significantly busier for each generation, so am happy if people keep in touch and stay in contact all year round, even if at busy times such as birthdays and Christmas they are more concerned with their own family units.