The early earth was as you describe, an ocean about the complete world only some meters deep and the crust more or less equalized. Tectonic activity started later in earths life.
This early state is named Eoarchean. As the earth was hotter after the formation of earth (energy of the cloud start crumbled together into the earth), in the geologic epoch before Eoarchean there was no crust at all, the rock was liquid (magma). In the eoarchean for the first time the earth had an stable crust, but it was very thin, so every movement of the magma below lead to fissures and assimilation of material and rebuilding new crust. So the surface stayed more or less even.
In later epochs the earth was cooling more and more, leading to a thicker crust. Now movements of the magma underneath didn't lead to assimilation of material, but parts of the crust moving against each other lead to warping of elevations. This process is named tectonics and is reason for the big differences in elevation you can find on todays earth.
So to answer the last question, no more cooling leads to even thicker crust and more potential for elevations, until the magma underneath cannot move the crust anymore. If that happens the difference in elevation will eventually be straightened by erosion. So you have the ideal world you describe early in earths life and late if the earth is cooled and tectonics don't work anymore.