A fair approach would be to allow me to use the thing for a day without "liking" it. Then they could say "Like it so far? Then click the Like button and listen

A fair approach would be to allow me to use the thing for a day without "liking" it. Then they could say "Like it so far? Then click the Like button and listen on!" and only after that keep me out if I don't. I don't think they'd get much fewer likes this way and at least they would be genuine. Plus, since more users would sign up to test the service, perhaps the numbers would even play to their advantage.