Inexpensive barometric sensors are _remarkably_ sensitive too. Like enough precision to detect less than 10cm or 4" changes in height/altitude.

Note that's "sensitive", not "precise". The atmosphere changes pressure with the weather, so you don't get accurate absolute altitude - at least not without knowing the local "pressure altitude". Barometric pressure can vary in a way that represents plus or minus 300 or 400m of altitude, and can swing between high and low fairly rapidly in extreme weather events.

But over short timeframe the change in barometric altitude can be very useful. Glider pilots (including paragliders and even RC gliders) often use very sensitive barometric pressure sensors to detect when they're in rising to sinking air, down at the few meters per minute range of sensitivity.