You still don’t know for sure that it needs inflated, because:
1. setting tire pressures incorrectly is not uncommon
2. That button is user accessible and might be pressed inadvertently or by someone who didn’t set the tires correctly
3. If all tires change in pressure at the same time, it would be undetectable
This is why these systems generally tell you to “check” your tires, rather than inflate a specific one. If they made that assumption, your car could be telling you to inflate an already overinflated tire.
There are many cars with tpms in the wheel that still won’t tell you what wheel it is or what’s the pressure, so I still much rather have no sensor to deal with trading the “inconvenience” of checking the tires once the light comes on, which is what you would do anyway.
I was explaining why the engineering of the system dictates the information that the interface provides.