This leads to the perverse situation in which less competent people rate their own ability higher than more competent people.
This is not what Dunning and Kruger found. A quick look through their original paper on the topic instead shows that most people rank themselves as being similar in ability; including the very best and the very worst performers. Observe the below figure:
Note that the fact often pointed out as the central point of the Dunning-Kruger effect, that the worst performers rate themselves as better than the best performers, is actually not true. The ranking by self-reported ability is the same as the ranking by actual performance; only the variance is grossly underestimated. Of the four experiments conducted in the original study, the biggest divergence from accurate ranking was experiment 2:
The top quartile still reported their ability to be higher than anyone else did; and the most important point again (to me) is how little variance there is in people's self-reported abilities.
It seems to me these experiments have been grossly over- or misinterpreted. All Dunning and Kruger showed was that the majority of people rank themselves as being a bit above average at everyday skills, regardless of actual ability.