What if the public funded it and tolerated the cost overruns, and the numerous delays because they wanted the "circus aspect" photography? Looking at you Juno and thanks for the swirling ocean photos on Jupiter. I bet the majority of the public did! YMMV
But the JWST will be returning some spectacular images: it's a telescope.
That's why I don't understand this debate. You'll be getting lots of spectacular images from the earliest moments of the universe. Is that clear? We are getting a time machine here. We're just not getting selfies.
What if the public funded it and tolerated
the cost overruns
OK. Let's assume unlimited budget. The public (or, at least, Congress) has already tolerated plenty of them on this project. So that's a very reasonable "what if."
You'd still face the hard payload constraints of the launch vehicle itself. Every kilogram and centimeter devoted to this camera system (and the associated power and shielding requirements) would represent kilograms and centimeters that would need to be chopped elsewhere. You'd need to compromise or eliminate other aspects of the spacecraft, and/or tolerate the increased complexity and risk resulting from the inclusion of a zero-science-value selfie camera.
I would expect HN readers, of all folks, to be really familiar with the concept of the harsh realities of engineering solutions for resource-constrained environments.
Anyway, the armchair spacecraft designers among us clamoring for a selfie camera might as well go full armchair spacecraft designer. Tell us which of the JWST's instruments you would have compromised or scrapped in order to accommodate the selfie camera.