I am actually not sure that this is true. I used to think exactly like you, that rotations are just piles of small translations with time varying directions, but there is a problem with this, linear momentum and angular momentum are two different conserved quantities. If it were the case that rotations are just translations then you should be able to get rid of angular momentum and its conservation and explain it in terms of linear momentum and I don't think that you can do that. Linear momentum is tied to the homogeneity of space while angular momentum is tight to the isotropy of space. You could actually do the exact opposite, say that translations are just rotations about a point infinitely far away, but I think that won't work either. I really don't know for sure, I mean I am not really, really, really confident about it, but as far as I can tell rotations and translations are fundamentally different.

Unaccelerated translations make only sense as relations between two objects but you don't need any reference to detect acceleration, you can just release an object from your hand and see if it drops to the floor because of gravity, hits the wall behind you because your space ship is accelerating or flies away tangentially because you are on a carousel. Rotation requires continuous acceleration (I am avoiding the term constant acceleration because only the magnitude is constant but not the direction) of all the particles towards the center of rotation or otherwise they would fly away tangentially. But if rotation requires continuous acceleration and you can always detect acceleration without reference to some other outside objects then you can always detect rotations and that is not true for translations, you can not detect unaccelerated translations.

It is the difference between velocities and accelerations and the fact that rotations always require accelerations that makes rotations more than just a pile of translations. You won't notice any difference if you translate everything in space by the same amount, you won't see any change if you rotate everything in space by the same amount, there is also no difference if you change the velocity of everything by the same amount but you will immediately notice if you change the acceleration of everything.

Or maybe that is at least partially nonsense, unfortunately I haven't yet mastered that topic myself.