The problem as I see it is that the experts are responsible for the backlash against expertise. I know it's fashionable to blame policy makers and political leaders, but they are still doing what they were put in position to do. Experts, however, have made a media-like move towards opinion making, not simply the hard work of science.
I think the root of it is that they are no longer willing to say that they do not know. And the coronavirus was a perfect opportunity to do just that. They just didn't know. Instead, they put out models that were based on incredibly thin data, and those models had sensational implications. Rather than recognizing those implications were hypothetical at best, they used the mere possibility of a catastrophic situation to justify catastrophic action. then, as humans are prone to do, they double down as their models fell apart. Because humans are prideful. if the experts had come out as soon as the data was starting to turn and said "our bad, this thing is nowhere near as dangerous as we thought it was, we should end the lockdowns immediately," then perhaps we would have a case for trusting experts. But they didn't.
This isn't the first time we've seen it either. They've been so catastrophically wrong on climate change that any good that could be done to the change that *is* based on science is probably lost. They've been wrong on diets as well. Overpopulation, peak oil, acid rain, the hole in the ozone, global cooling, they just keep getting it wrong.
That's fine, science is messy, and in the long term it always tends towards progress, but in the short term it is frequently, if not more often wrong. The problem is, they don't want to admit that because it would mean a loss of authority. Power is a hell of a drug.
You should trust an expert when they are interpreting a historical body of work in their field. When your doctor says your cholesterol needs to be fixed, you should trust him. when a structural engineer tells you that you need a foundation of a certain thickness, you should trust her. But if a UFO lands in your backyard tomorrow, there are no experts. New things seldom have the luxury of experts.