Standard resistors come in many standard values and many power grades, meaning you can pick a resistor that minimizes source current for your application. Incandescent bulbs come in different rated voltages and powers, but they are far from precise or standard.
Depending on the design, shunt regulators come with short protection for free without relying on a PTC fuse (incandescent bulb or otherwise). You’re absolutely correct that the positive tempco of a bulb will reduce short circuit current, but how by how much and whether it is worth it depends on the application and the properties of the bulb itself.
I watched through it and I don’t understand what he is trying to do. It sounds like he is maybe trying to make a resonant tank but I can’t be sure.