I’ve seen quite a few critiques of the practicality of time complexity analysis but I’ve never seen an article describe what we should replace it with. Time complexity analysis, as given, has given some structure to the infinite zoo of problems even if imperfect and composes relatively nicely and is relatively simple. It’s also tractable, has mathematical structure, and is often practical as a heuristic (the kinds of algorithms people typically encounter or come up are typically reasonable under this kind of analysis). In order to be a proper substitute, something would have to satisfy all these qualities. Without such a substitute, we are back to analyzing problems and their complexity without any sort of framework which seems even worse than just remembering that sometimes the big O is not practical.

The only candidate that would be more practical that I know of is cache complexity for cache oblivious algorithms but that’s much more complicated.

Implicit Computational Complexity deserves to be more well known.