If you put a cup of water in a strong enough gravity, lower part of the cup will have higher pressure, and that part will turn to unusual ice types. While top of the cup will remain liquid. Cranking up a gravity will only change the ratio. This is why people use pressure instead of gravity, pressure is what defines the state.

Your main point is something like "material becomes weak compared to gravity, conforms to the cup, as if liquid", or "cant have long range structure". But we already have solids that are like that - sand. Sand doesnt resist change to its shape, it just slides in a new position. And yet we still consider sand to be solid. Angle of a pile in particular.

Even a neutron star likely has surface level irregularities on a scale of centimiters. While a liquid can flow to submicron level smoothness even in a diy experiment.

Material gets stronger as pressure is increased. Unusual crystal structure becomes available. Superconductors and some other weird properties can exist only when crystal structure is compressed. And this tendency continues all the way to degenerate matter, as in neutron stars. Material from inside of a neutron star is likely the strongest a material can be in this universe.

So in the end, "solidness" continues to fight back, presenting enough properties to differentiate it from a true liquid, even if it could look somewhat similar, "shallow pile of material", all the way to degenerate matter of neutron stars.