It's possible that an incorrectly fixed pothole would a) degrade far more quickly and b) do so in a manner that expands the pothole more than just leaving it alone would have.
Right. It's not so much about the pothole today, as much as it is the health of the entire road over the next decade+.
That said, addressing this and other concerns isn't rocket science. The city could easily publish a detailed guide to filling potholes (what materials are ok, what materials are not, what process to use, etc).
Publishing a guide to filling in potholes seems like it would create controversy with the public, who would ask why it appears the city expects citizens to fill in potholes themselves.
It's much easier to just allow citizens to call a number and report a pothole. Seattle does that and potholes get filled fairly quickly, they even have a phone app that allows you to report all kinds of problems.
Here's Seattle's pothole map showing where and when they have been fixed.
You could publish it in a way that was more "How we repair our potholes." Include the types of materials, the procedure, etc. This would mask it so that you could plausibly deny encouraging citizens to self-repair.
Council crews everywhere could realistically have best-practice blogs detailing all sorts of stuff to encourage residents to aim for a certain standard (verge upkeep, etc) or achieve other targets (water usage and the like).
