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.
It's certainly not true in principle that most problems in P have a small exponent. There is no shortage of graph related algorithms in P that have absolutely absurd exponents, like on the order of 10^100. It is true that practical decision problems that are in P have small exponents but that's exactly the point being made, namely that problems in P with large exponents are not practical and hence don't get much attention.
In many applications, the data grows at least as quickly as computer performance. If the fastest known algorithm is superlinear, today's computers take longer to solve today's problems than yesterday's computers solving yesterday's problems. While O(n^2) time algorithms used to be pretty fast in the 80s, today they are often unusable.