For a high synchronized rate of fire, the time interval between the pilot ( or the interrupter gear) pulling the trigger and the shot being actually fired has to be as short as possible. The Ho-103 was a Browning derivative and as such fired from an open bolt, meaning that the bolt had to run forward and lock before the round was fired. Most other aircraft machine guns fired from a closed bolt so the shot went off at once. I don't think it was possible to decrease the mechanical inertia of the Browning mechanism enough to get a significantly higher ROF while synchronized. Almost all British or US aircraft used Brownings unsynchronized (outside the propeller disc(s) ) for that reason