The link to delay is still there: You are absolutely right, we should delete it in case you're already delaying. (Actually, I already made the change on a test environment)
Adding a separate status for 'delaying' has a lot more impact. The travel page clearly says you're already delaying though.
How much? I remember when it was first implemented, I would always double check a ton of times, because the game implied it hadn't worked and that I wasn't truly delaying. Now, I've gotten somewhat used to it, but it really seems like a lot of people get played.