Even if you test manually what you just changed, in a relatively complex codebase how can you guarantee that your changes haven't broken behaviour in a separate yet related aspect of the system?

This is what I find the major advantage of a comprehensive test-suite to be, I don't have to worry as much about breaking any part of the system as a whole - if my suite passes, then I know everything I've worked on so far works, not just the bit I think I changed.