Not quite bubble sort, but many recursive sorting implementations will switch to an O(n^2) algorithm like insertion sort once they reach a small number of elements. Simple but poorly-scaling methods usually have a place as base cases of hybrid algorithms.

In other news, there's a reason no BLAS implementation multiplies matrices with Strassen's algorithm, and it's not that the people writing those are too dumb.

Still, in quicksort, big O notation analysis is what tells you that you can further improve efficiency by leaving small subarrays unsorted and then performing a single call to insertion on the whole array at the very end, rather than one insertion call to sort each individual small subarray. This result is far from obvious without big O analysis. So still useful, even there.