So in the end it is largely a question about how smart the python implementation is or is not, particularly in the case of the inner function not being a closure but simply an in function needed helper only.
In clean understandable design having functions only where they are needed and not exposed elsewhere is good design whether they be embedded in a module, a class as a method, or inside another function or method. When done well they really improve the clarity of the code.
And when the inner function is a closure that can also help with clarity quite a bit even if that function is not returned out of the containing function for use elsewhere.
So I would say generally do use them but be aware of the possible performance hit when you actually are concerned about performance and only remove them if you do actual profiling that shows they best be removed.
Do not do premature optimization of just using "inner functions BAD" throughout all python code you write. Please.