Many years ago, as an undergrad, I had a conversation with a grad student friend about the Selection algorithm (which will find the kth largest item in an unsorted list in O(n) time). I loved it, but when I tested it in practice it was slower than just sorting and selecting well into the billions of elements.
My friend said "that may be true, but consider the philosophical implication: because that algorithm exists, we know it's possible to answer the question in O(n) time. We once didn't know that, and there was no guarantee that it was possible. We might still be able to find a better O(n) algorithm."
I feel the same way about this. Sure, this might not be faster than Dijkstra's in practice, but now we know it's possible to do that at all.
My friend said "that may be true, but consider the philosophical implication: because that algorithm exists, we know it's possible to answer the question in O(n) time. We once didn't know that, and there was no guarantee that it was possible. We might still be able to find a better O(n) algorithm."
I feel the same way about this. Sure, this might not be faster than Dijkstra's in practice, but now we know it's possible to do that at all.