This is a follow up to my previous question:
I find it bewildering that we haven't been able to prove any quadratic deterministic time lower bound for any interesting NP problem that people care about and try to design better algorithms for. Our Exponential Time Hypothesis conjecture states that SAT cannot be solved in subexponential deterministic time, yet we cannot even prove SAT (or any other interesting NP problem) requires quadratic time!
I know interesting is somewhat subjective and vague. I don't have a definition. But let me try to describe what I consider to be an interesting problem: I am talking about problems which more than a few people find interesting. I am not talking about isolated problems mainly designed to answer some theoretical question. If people are not trying to find faster algorithms for a problem then it is an indication that the problem is not that interesting. If you want concrete examples of interesting problems consider the problems in Karp's 1972 paper or in Garey and Johnson 1979 (most of them).
Is there any explanation for why we haven't been able to prove any quadratic deterministic time lower bound for any interesting NP problem?