I completely agree with you. My point was that the P vs NP distinction matters in practice, but of course also the subquadratic vs quadratic time distinction matters a lot.
What are examples of natural graph related problems in P with absurd exponents? I think the reason they don't get attention is not that the algorithms are not practical, but that the problems are not natural. Really, the only examples of such problems I can think of are something like "Finding a clique of size 222222 is in P because we can try all possibilities in n^222222 time".
I'm not sure if its really misunderstanding, when in 99% cases it has turned out that if a problem is in P, then it has a polynomial-time algorithm with a quite small exponent.
For binary-encoded input it is in 2-EXPTIME by trying all graphs of size exponential in the input number and testing all subsets of the given size. Would be surprising if any hardness result for complexity classes would be known.
I read the essay, and my takeaway to "There are for example four fundamental forces. Are we going to find another four?" would be:
Maybe not, but we could find out that the model of fundamental forces wasn't really the final answer, and explain the universe much better with some alternative theory. In your comment you assume that science is more or less settled, and all there is to do is to tweak the present understanding a bit and fill some gaps. The same sentiment was shared by many prominent physicists already in the end of 1800s, who were obviously proved wrong by Einstein and others in the 1900s.
Well, it is also not proved to not be NP-hard, so it could also be NP-hard to our current knowledge. But you are right that researchers believe that it's not NP-hard.
Is there some fair comparison of D-Wave annealer vs classical methods on optimization problems? I remember seeing papers where it was compared to some naive methods or the runtime of D-Wave approximation algorithm was compared to the runtime of classical exact algorithm -- obviously apples vs oranges.
The sycamore is really on the border of what current classical methods can simulate. You also need to consider that the funding used for building sycamore was probably orders of magnitudes larger than the funding used to build classical competitors.
>There's no real big theoretical problems in the quantum computer building space
The current quantum computers are just on the edge of what we can simulate classically, so we can't yet rule out the possibility that realizing a quantum computation requires an exponential amount of energy in the number of qubits. (Though it should be noted that quantum mechanics predicts that this will not happen.)