I'd say this is the most optimistic scenario. there are really difficult problems to be solved in terms of access to AI.

The idea that most any modern "interesting" aspect of mathematics is going to be understood (or often even explained in enough detail to reveal what is interesting) in an hour is pretty rare. Either the student's aptitude, the tutorial, or the mathematics are unique. There is a reason that these are PhDs and not undergraduate HW sets.

I think we often delude ourselves as to how well we understand problems and their solutions. Some instructors even make you feel that you understand better than you do by pointing to a few approximations or simple solution spaces that obscure the larger complexity. Just looking in wonder at the many categories of three-body solutions (currently on hnews) is enough to remind me of this.

> the "rigorous defense" part

In my country, that's exactly how it is.

Yes, you need to have a thesis to defend, but ultimately it all comes down to the (oral and live) defense/disputation.

Why is "Doctor of Philosophy" the correct certificate of "becoming expert in a topic"?

That's a radical departure from "PhD" being a certificate that someone is qualified to produce new research.

What you describe is more like a Masters Degree.