The lamp intensity won't vary in a shunt regulator because the current through the shunt resistor is constant. The current through the zener diode varies to split that current with the load. Otherwise, yes it will work, however you will have fewer choices of resistance and will not be able to make the regulator as efficient.
this post was submitted on 21 Jun 2023
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Any particular shunt resistor that you have in mind? You are correct that the lamp brightness would remain the same whilst in the regulated zone. I was more thinking of operation outside that region - eg in a short condition. Having a lamp as the series resistor would reduce the fault current compared to using a fixed resistor.
Not sure what you you mean by "fewer choices of resistance". The lamp would be the series resistor - other than that, what resistor did you have in mind?
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.