That is what I do for most back-end tasks (not so much for front-end stuff yet although there is some interesting work happening in the open source world for that too). And I've actually had far fewer bugs testing with TDD than testing in browser.

In the browser, testing edge cases sometimes requires custom headers, encoding of data to create authorization tokens, etc. This means you have to either have amazing browser tools (which I've yet to find) or use a combination of browser and shell to achieve what I need.

In TDD, most setup can be automated with simple function calls. In addition, well made frameworks, such as PHP's Symfony, have utilities that even avoid making real HTTP requests, so tests run faster than using a browser, but the result is the same.

I'm not saying everyone should do TDD, but from my experience, it can lead to increased productivity and fewer bugs in some cases.

By the way, if you know of browser tools that make testing easier, I'd be glad to learn more. I use TDD because I lack the browser tools. If I had the right tools, maybe I'd consider going back to in browser testing.