Why doesn't hydrostatic pressure glue objects to the seafloor?

I'm assuming from your drawing that $F_{SeafloorResistance}$ refers to the normal force that the seafloor applies on the bottom of the block when it is resting on the seafloor. Your question seems to be "what is pushing on the bottom of the block if it is not touching the seafloor but also has no water beneath it?" This question seems to be an illustration of what happens when the idealized "frictionless plane" world of physics class runs into the slightly messier reality in which we live.

The same hydrostatic pressure experienced by the top of the block is experienced by the sides of the block as well, but of course this does not contribute to the net vertical force. In "the real world", this pressure would cause water to fill in all cracks and crevices at any opportunity, allowing water to get beneath the block and balance the downward force from the hydrostatic pressure above.

Now you stipulated that everything is "perfectly polished", presumably meaning there is no crack or crevice through which water can flow. Let's imagine there is dent in the middle of the bottom face of the block with no air in it (a vacuum); the dent can be as small as you like. Your idealized, completely smooth (except the tiny dent), un-deformable block has just become the perfect suction cup. In this case, you are right that much more force would be required to lift the block: the force would be $A \cdot P$, where $A$ is the area of the top surface of the block and $P$ is the hydrostatic pressure of the seawater.

(Note: you don't need the dent at all: as long as there is no water pushing below, you will have a suction cup scenario. I just put the dent there to conjure up the image of a suction cup.)

It wouldn't matter if we were talking about air, water, or any other fluid. If no fluid is allowed to penetrate between the surfaces in contact, it's like a suction cup; the weight of the fluid column above the object (and of the object itself) is balanced by support from the floor beneath. To raise the object, you'd have to overcome that force.

There is a scenario where you can see this... when you get your boot stuck in mud at the bottom of a puddle. The force you need to extract your boot is equal to the weight of the air column + water column over the surface you are trying to separate (give or take the weight of the bit of mud covering it).

The connection between the boot scenario and the concrete block scenario is that mud (fine particles and water) will resist the flow of water (and can impede the transmission of hydrostatic pressure) because of surface tension and capillary action. When you pull up on your boot, the mud doesn't want to flow, and neither does it allow the water flow in under it to balance the hydrostatic pressure acting above it. So you have to overcome the hydrostatic pressure from above to get your boot free.

In fact, hydrostatic pressure CAN 'glue' objects to the seafloor. Seabed surface soils have an attribute called permeability. For the sake of your model, you can think of it's affect as billions of little plungers attached between the bottom of the block and the soil and having a very low flowrate of water into them.

As upward force is applied to the object, the plungers (cohesively attached to the block now; assuming clay) attempt to fill with water at a slow, fixed rate until a) the strength capacity of the plunger is exceeded and it breaks off (the cohesive strength of the soil) or b) enough time passes that the pressure in the plunger is reduced from the pressure exerted by the blocks weight down to the ambient seawater pressure, at which time the plunger is no longer suctioned to the surface.

Thus, in clay soils it is required that the cohesive soil capacity is included in the lift capacity of the rigging used. An additional capacity for a soil 'plug', or section of soil which may stick to the object, is added since the failure plane of the soil will typically not be between the block and the soil, but soil to soil (i.e. a layer of soil will remain stuck to the block, especially if it has a skirt around the bottom).

For objects placed on sand (or cohesion less soils), this is essentially not applicable, since the increased permeability (associated with lack of cohesive strength) allows water to flow at much higher rates through the soil, alleviating the issue.