Film formation in a water-based system happens in three stages. First, water evaporates and the particles concentrate until they are in close contact. Second, capillary forces from the remaining water press the particles together hard enough to deform them. Third, polymer chains diffuse across the particle boundaries and the interfaces disappear, producing a genuinely continuous film.
That third stage is the one that takes time and temperature. It is why a water-based coating can feel dry to the touch long before it reaches full properties — the particles have packed but not fully interdiffused. Full property development can take days.
Coalescing solvents work by temporarily plasticising the polymer so the particles deform and interdiffuse at a lower temperature, then evaporating out of the film afterwards.