Why do planes above FL290 need more vertical spacing?
The atmospheric pressure changes more rapidly with altitude near the ground than it does higher up.  Assuming an instrument has some error based on determining the difference between two pressures, this error increases with altitude.

Using a standard atmosphere, the pressure difference between 3000 and 4000 feet is 3.3 kPa.  The difference between FL290 and FL300 is 1.4 kPa, less than half.