The only drawback I can see is continually resetting it when you raise and lower your tyre pressures for towing, unless you set them with a general tolerance. How long do your batteries last in use and how long does the screen hold charge for.
In reality, in our context, it only matters critically if your tyre pressures drop. That, they increase in pressure and or temperature when in use are facts of life about which you can do nothing and in all honesty most of us know nothing about the real relevance.
However, the pressure dropping from the cold inflation pressure, whilst in use really means a puncture.
So with the question about changing set values for towing solo and indeed loading is all of no importance or needed, set to the lowest of all these, minus a psi, and if the system throws up a warning you need to act toot sweetly.
The unit displays the running value so you can monitor the actual value if really academically interested in the situation under differing running conditions and mentally compare it with what you know it ought to be.
You will very quickly see a pattern of how things change with running, ambient, sun-side, rain, speed, road condition, towing and vehicle loading. Be prepared to see big changes on the caravans highly loaded tyres.
As said, the only thing that matters is knowing they don't drop, only that without being a tyre scientist can mean anything to need getting a warning about.