this isn't any better than using a live server for testing.
Build a good client library for your applications to use, mock the client library and don't worry about tests failing because of availability problems.
If the live server has side effects when making the call (send an email, charge a card, etc) and you just want to test against the response headers/body, it can be very useful. A local mocking library is also good for that, but for quicker tests this is nice.