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For large-scale weather you can directly invert them using forms of the hydrostatic equation.

$$\dfrac = -\rho g$$ Basically this proves extremely accurate when vertical acceleration is small, which is generally anywhere outside of intense thunderstorms.

it could well answer that question of why they chose to record at equally spaced pressures instead of heights in early ballooning.

This is because, despite being called "surface maps", they're actually sea-level pressure maps.Or when radio and the early instrumentation were developed, what would draw them to choose set pressures or set heights?I don't know the history well enough to give a certain answer to that.In the end, it probably goes back to how early upper-air observations were recorded.It may well have been some guy going up in the balloons until radio, so would they have recorded at equal heights or equal pressures?

Invalidating decsa