Bear in mind that the Headstock bearings may not have been designed for higher speeds. Correct and adequate lubrication is a necessity for any bearing, but becomes more important as speed is increased.
As already said, a higher spindle speed will mean that less torque is available for cutting. Another reason, if needed, for keeping tools sharp. (And replaceable carbide tips are not sharp in the way in which HSS tools are, or should be).
Howard