I think one of the unsaid concerns here, for those of us that worry about these things and just aren't "out to be noticed" is the offhand chance that the couple thinks you came to their wedding and didn't show up with a gift at all. Weddings certainly don't demand a gift, but we all know that it's customary to bring one. That could be changing. I got married in the 80s and I don't recall it being a thing NOT to bring a gift. My wedding was very large, lots of guests, and before the days where people shipped things to your home with ease. We had a big gift table because people did more gifts rather than money, and we had a card box. The next day, with a crew of people, my DH and I opened the gifts and everything was cross-checked against the guest list so that we could make sure that nothing was lost or whatever (as I said the reception was quite busy) and I made a specific list of what each person brought so I could personalize my thank yous. We had one guest that had no gift and this was not a person that you would ever think would NOT bring a gift. It was a friend of my parents, not someone close to me. I didn't know what to do and I certainly didn't want to ask her if she brought something and it was missing, but I would have loved if she had approached me about it if she didn't receive anything from me. I've always wondered about it, but I sent her a note anyway and thanked her for coming and hoped if there was a missing gift that the acknowledgement somehow covered it.
So, yeah I'm always concerned with #5 or #6. I like to write a check and if it's cashed then I don't worry about it, and move on. I've only had once instance where I was never thanked and that was by my cousin and his wife. Sent them baby gifts through the mail also and never know to this day if they were received. But whatever, I wanted to do it and I don't care. I guess I worry to much about things getting lost or misplaced.