I can only speak from my experience (20 years) of developing web apps, but I've never seen a cohesive, loosely coupled web app, that was both over 2 years old AND not using some form of TDD.
Phrased that way, I agree completely. An established codebase needs to be verified in some ways. But writing code and running it against tests is not exactly equivalent to TDD.
TDD as I understand it is characterized by writing a failing test, followed by implementation code, followed by test-fixing, etc.
However, I can write plenty of good code that does what it's supposed to and works and is stable. THEN I'll refactor as needed, write tests, and since I anticipated my needs, making those tests good and the code testable will be relatively straightforward. That's not TDD, though. It's a pragmatic approach that doesn't prioritize setting requirements (or solidifying an API) over starting simple and iterating quickly.
