Motion allowed for hunting and grazing. No joke!
Many single-celled prokaryotes like bacteria and single-celled eukaryotes like the Paramecium developed a propeller system, i.e. flagella and cilia.
Paramecium or paramecia are single-celled protists that are naturally found in aquatic habitats. They are typically oblong or slipper-shaped and are covered with short hairy structures called cilia. Certain paramecia are also easily cultured in labs and serve as useful model organisms (a non-human species used to understand biological processes).
The single-celled slime mold developed pseudopodiai.e. walking.
and many amoebas.
A pseudopod or pseudopodium (pl: pseudopods or pseudopodia ) is a temporary arm-like projection of a eukaryotic cell membrane that is emerged in the direction of movement. Filled with cytoplasm, pseudopodia primarily consist of actin filaments and may also contain microtubules and intermediate filaments.[1][2] Pseudopods are used for motility and ingestion. They are often found in amoebas.
The interesting part is that all modes of propulsion are facilitated by microtubules which are present in ALL eukaryotic organisms.