Mechanical character progression matters to me and most players simply because the game accepts it. Higher levels, stats and more upgrades make the game easier and thus making achieving goal easier also. Then in higher level/stage/map/world, there are more stuffs, more XP etc which is easier to gain with higher stats which creates the basic game loop.
So yeah, this simple loop gives motivation for players to keep playing.
As for satisfying game without levels/stats/whatever, well it depends on the focus of the game. If the game focuses uncovering more areas and it could be done without levels/stats/etc, exploration could be satisfying.