What's missing here is something has to maintain the pressure at the "entry" and "exit" points of a flow. Generally, depending on the source of the pressure, an unrestricted flow will have less pressure than a restricted flow, but the higher pressure related to a restricted flow occurs prior to the restriction, and it's only within the constriction that the velocity increases and the pressure decreases. Once beyond the constricted section, the velocity decreases and the pressure increases, but there needs to be something to maintain the pressure beyond the restriction, and in order to have a steady non accelerating mass flow within a pipe of constant diameter except for the restriction, the pressure before and after the restriction needs to be the same, and something needs to maintain that pressure.
Consider that static pressure is related to the random collisions between molecules of a fluid or gas, and between those molecules and the inner walls of a pipe. Assume that the total mechanical energy is constant, which is an assumption required for Bernoulli's equation. If there is a net velocity of the flow, then some component of the mechanical energy is related to the net velocity (this would be dynamic pressure * volume). The higher the net velocity, the lower the components of velocity perpendicular to the flow, so that the "randomness" of the flow is "reduced", the flow is more "organized". The static pressure is changed when the net flow velocity is changed, if the net flow velocity increases, then the static pressure decreases and dynamic pressure increases (total pressure = static + dynamic pressure remains constant) assuming no outside work is done during the transition.
