There’s a section in the greeting card store for “New Baby” cards. I’m not sure what other kinds of babies are available. But the ‘new’ reminds us of why we are sending the card.
And “Happy Birthday” goes without saying as well. The person knows it’s their birthday, and of course you want it to be a happy one, that’s why you sent a card. While a blank on the front of the card would probably have just as much information value, saying it more often than is necessary is precisely the point of the card.
Sometimes, we assume that the person we’re engaging with knows exactly what we mean and want to express. But that assumption is often wrong, and a little redundancy can go a long way.