Why vacuum instead of pressure to power gyros?
There are piston aircraft that use positive pressure to power gyros.  The Beech Baron and Bonanza lines as well as the Piper Navajo line use pressure instead of vacuum. We're not talking about one-off airplanes here!  The Baron/Bonanza and Navajo are some of the most popular airplanes in their respective categories which, when summed, total many thousands of airplanes (and pressure pumps).

The turbines I've flown used ejector pumps, not mechanical pumps, to draw vacuum so I will assume that this class of plane is out of scope for the purposes of this question.

A technical answer to your question will require an aircraft system engineer (perhaps Peter?) to weigh in.  My guess is that vacuum pumps were installed to replace venturis.  Since systems (and instruments) were already designed to run vacuum, the pumps were installed to draw vacuum instead of apply pressure.  Why change what works?