By increasing the bleed demand, you reduce the pressure of the air in the compressor for the same engine RPM. Similar effect as reducing your weight whilst flying at the same IAS - your stall margin is bigger.
agree
but the major effect of the ash is the closing down of the Turbine inlet vanes due to plating of the remelted ash on the stationary turbine inlet vanes. Thus the concern is to reduce the turbine inlet temperature (by throttle back) before the ash builds up and to reduce the compressor output pressure in case the ash has already built up.