If you really want to keep using the analogy, it's like you going to a restaurant and they require you to take a taxi to the actual location (and tell you the cost upfront), and you just take it then refuse to pay.

You do have the option of not using a service that uses recaptcha. Nobody is forcing you to fill them out, you are making the choice to do it because you want the service the site owner is providing, and the site owner wants recaptcha.