TBH I think there is an important structural difference, other than the loading screens.
In Prime 1 you did a healthy chunk of the Chozo ruins (did not finish them), went quickly through Magmoor Caverns as en-route to Phendrana, did a chunk of Phendrana, returned to the overworld, and so on.
In Prime 2 and 3 you largely worked on one unified area and then moved on to the next at a regular clip as opposed to working your way through the labyrinth in an irregular fashion.
Sure, you went back to Icy Bryyo and in Echoes I think there was always a quick jaunt back to the previous area, but 2 and 3 were very much "temple" oriented, like a Zelda, whereas Prime 1 was more unpredictable. You had your extended journeys, your action set-pieces, your through-visits, your unguarded power-ups, your bosses, etc.
In Prime 1, you are repeatedly weaving the world together with your through-travel.