Examples of collapsing hierarchies
The analogue of the $\mathsf{NC}$ hierarchy for algebraic circuits is known to collapse to the second level. That is, algebraic circuits of size $n^{O(1)}$ computing a polynomial of degree $n^{O(1)}$ can be rebalanced to have depth $O(\log^2 n)$ while only increasing the size by a polynomial factor. This is due to Valiant, Skyum, Berkowitz, and Rackoff. It is open whether $\mathsf{NC}^1 \stackrel{?}{=} \mathsf{NC}^2$ in this setting, but I believe the popular opinion is that $\mathsf{NC}^1 \neq \mathsf{NC}^2$ here.
If one further restricts to syntactically multilinear algebraic circuits, then we in fact know $\mathsf{NC}^0 \subsetneq \mathsf{NC}^1 \subsetneq \mathsf{NC}^2 = \mathsf{NC}$ unconditionally. The fact that $\mathsf{NC}^1 \subsetneq \mathsf{NC}^2$ is due to Raz, and the fact that $\mathsf{NC}^2 = \mathsf{NC}$ is due to Raz and Yehudayoff.
Raz, Ran, Separation of multilinear circuit and formula size, Theory Comput. 2, Paper No. 6, 121-135 (2006). ZBL1213.68301.
Raz, Ran; Yehudayoff, Amir, Balancing syntactically multilinear arithmetic circuits, Comput. Complexity 17, No. 4, 515-535 (2008). ZBL1188.68367.
Valiant, L. G.; Skyum, S.; Berkowitz, S.; Rackoff, C., Fast parallel computation of polynomials using few processors, SIAM J. Comput. 12, 641-644 (1983). ZBL0524.68028.