You are bounded by a minimum floor for the hot water. Below a certain point you can get legionnaires.

To me it seems like one of two things: external pressure between hot and cold is mismatched so a small change to one side overwhelms the weaker flow.

Alternatively it might just be a broken or poor quality mixer that isn’t providing the appropriate ‘nuance’ of control, and that may indeed be expressed as some sort of non-linear relationship.

> Below a certain point you can get legionnaires.

I know you mean legionnaires' disease, but the idea of a bunch of soldiers getting to your house because you turned your boiler too low made me chuckle. Good thing the US have the third amendment to protect against this.

The thermostat could still be set too high. I think you might be overstating the dangers of legionnaires.

It also a simple thing to check and would be the first step in my troubleshooting routine for this complaint.

Here is a link describing the dangers.

https://www.heatgeek.com/hot-water-temperature-scalding-and-...