I'm not a fan of thank you cards, especially from a 4 year old. If a child has to be "made" to write them, they're not sincere and I don't really want one.
If my DD asked to send them, then obviously she would. Although I wouldn't believe it would have come from her, it would have been MIL in her ear - but that's a different matter.
I don't assume that someone has bad manners because they don't send a thank you card. I didn't send them after our wedding, we had other circumstances going on and anyone who was that offended by the fact, I'm not bothered about anyway.
MIL once told us about how their friends wouldn't send a gift for a couple's new baby because they hadn't sent thank you cards after their wedding (may well have been about us, I don't care) which I thought was especially rude. I don't send a gift to receive thanks, if I give a gift it's about the giving, not what I might get in return.
So, although it's nice to receive them, I would never expect one, and I wouldn't want one that was forced and insincere anyway.