It would have been lovely to have at least some data from mortality tables pre and post. I guess record keeping wasn't on their mind.

Probably helped reduce infant mortality from casual enteric disease risks, and things like shigella and worms, as well as maybe some communicable skin diseases.

I'm unsure it could have ever been enough to stop pneumonic plague, bubonic? If they kept the rat population under control maybe it had some upside?

Policing population flows and inspections of goods to market was pretty common. Pre plague licence to operate a market was a tax revenue monopoly function. Post plague with the labour shortage it probably was essential to either encourage journeymen to settle or hold a market for non locally produced goods.