First, let me say that what we are discussing at the moment, percent-level inequalities, does not even depend on metric units. Those issues also are there when using imperial units. Just often ignored. Which is OK. It is actually not even a given that pressure sensors measure to percent precision.
This being said: using bar instead of atm also does not eliminate the issue. The bar is fixed to be 10^5 Pascals. And the Pascal is a force (measured in Newtons) per area. If one liter of freshwater weighs 1kg, a 10m column exerts 0.98bar. Not 1bar.
Having the pressure double after the initial 10m is convenient, this is the attraction of the unit atm. But it will never be perfect any way.
In practice? Let the dive start at 1bar and add 1bar per 10m. Happy dive, happy life.
This being said: using bar instead of atm also does not eliminate the issue. The bar is fixed to be 10^5 Pascals. And the Pascal is a force (measured in Newtons) per area. If one liter of freshwater weighs 1kg, a 10m column exerts 0.98bar. Not 1bar.
Having the pressure double after the initial 10m is convenient, this is the attraction of the unit atm. But it will never be perfect any way.
In practice? Let the dive start at 1bar and add 1bar per 10m. Happy dive, happy life.