The paper book catches a fraction of the love
Think about how a physical guest book actually gets used. It sits by the door, it gets signed by the thirty people who notice it, and the note your aunt wrote on the train is in a coat pocket by the evening. The quiet cousin abroad never sees it at all. The whole thing depends on timing, pen and a free hand at the right moment.
An online guest book asks none of that. Anyone with the link can leave a wish when it suits them — the day before, on the morning, a week after, from another country. The messages gather in one place you control, moderated so only what you approve shows, and they are still there to read years later, which is more than the paper one usually manages.