I see it as a failure of the model. When the explanation is irrational, does a scientist stop to wonder at the irrationality of the universe instead of trying to come up with better explanations?

While I agree that science is currently seeing only small part of the picture, I don't believe scientists have stopped trying to find explanations.

And what is more important - it's very hard to judge if the explanation is rational. Every science is built on some axioms which define what is rational and what is not. That's why I guess the progress happens step by step (each next step expanding what one would consider rational).

Thousands of people have been trying for 50 years. Every model they've tried has turned out to be wrong.

It's easy to say "come up with better explanations". It's not very helpful, though.

It's easy to dismiss criticism by complaining that it doesn't propose solutions, but the two are distinct and unrelated activities.

The purpose of criticism is not to be directly helpful by proposing better solutions, but to help eliminate the wrong ones.