After really reading through this, I can't believe how many people are so put off by this! Don't you LOVE the people you're going to these showers for? Don't you spend enough time with them to know how stressful it is to plan a wedding or have a new baby? Does it really inconvenience you THAT much to take 20 seconds to write your own address after you've already put yourself out SO much by buying a gift, showing up, and writing your own card that it angers you to be asked to do so and save the bride some time? Something that could easily add a half hour + to their thank you card writing time.
I'm happy to go out of my way to help people in that situation, because I've been there and know what it's like. I don't feel annoyed by "tackiness", I'm happy to have an opportunity to help. If you're not, maybe you don't belong at the shower.