Why do our bodies maintain blood pressure but not the flow rate?
A constant blood-flow would not be advantageous to organisms with a varying activity level. The blood supplies (mainly) oxygen to the tissues and the supply of course needs to match the requirements. Organisms rely on a number of mechanisms to ensure this match, one of these is to increase the blood-flow (heart-beat). But flow through a (blood) vessel relates directly to the pressure and inversely to the cross-sectional area of the vessel, so if the flow is increased, the organism must accept either a higher blood pressure or expand  the blood-vessels. Of course, it is in reality a compromise of both mechanisms.