So using TDD to drive new features will force you to correctly use (internal) functions.
Exactly. But keep in mind the subtle "gap" here: you should use TDD to write (unit) tests that test the contract of your public methods. You do not care about the implementation of these methods - that is all internal implementation detail.
Therefore: if your "new" code uses an existing method in an unintended way you are "told" because an exception is thrown or you receive an unexpected result.
That is what I mean by "gap": you see, the above describes a black box testing approach. You have a public method X, and you verify its public contract. Compare that to white box testing where you write tests to cover all paths taken within X. When doing that, you could notice: "ok to test that one condition in my internal method, I would have to drive this special data".
But as said - I think you should go for black box testing - white box tests might break easily when refactoring internal methods.
And there is an additional dimension here: keep in mind that ideally you change code in order to implement new features. This means that adding new features only takes place by writing new classes and methods. This means that your new code has no chance using private internal methods. Because you are within a new class. In other words: when you regularly happen to run into situations where your internal methods are used in many different ways - then you are probably doing something wrong.
The ideal path is: you implement a new requirement by creating a set of new classes. Later on, you have to add other requirements - by writing more classes.
In that ideal path - there is no need for defensive programming within internal methods. Because you exactly understand each use case for such internal methods!
Thus, the conclusion is: avoid defensive programming in internal methods. Make sure that your public APIs check all pre-conditions, so they fail (as fast as possible) if there is a problem. Try to avoid these internal consistency checks - as they tend to bloat your code - and rest assured: in 5 weeks or 5 months you will not remember if you really needed that check, or if it is just "defensive".