What is the physical significance of both options. When to use static pressure (fixed every where) and when to use the Average static pressure(floating with average constrained)?

In my opinion static pressure condition may be the good for the boundary far away from the object to be studied, in other words flow is more or less uniform at outlet boundary.
On the other hand the average static pressure may be more physically correct as it allows the conditions to vary along the boundary. This can be the situation in nozzle (may be diffuser, compressor, turbine, combustion chamber) where the velocity is higher in centre and low in the wall region. In other words pressure may change along the boundary so as to capture the true picture of flow form the interior and at the same it also forces the mass flow to be some average value (also changes from cell to cell) corresponding to average value of static pressure on whole boundary.