Ecology is incredibly difficult because everything is horrendously under-sampled. Essentially all ecology reduces to counting species over time and somehow extrapolating to huge areas. So-called total count surveys are extremely expensive.

I can only speak from a megafauna perspective (eg not insects), but there were recently some results that suggested that animal decline in Africa was overestimated. Caused quite a stir. And it makes sense when you learn how people count animals in aerial surveys - photographic interpretation is novel because most ecologists are not used to dealing with that level of data, nor the complexity in designing the camera systems, and it was impractical to do with film in the past. The gold standard is someone with a voice recorder in a plane. When you actually go through aerial photographic surveys, you spot all sorts of things that the observers missed, because they're not superhuman. That's not to say there is no decline - poaching has still decimated populations - but for some species it might not be as bad as you think. In theory the methods (things like JOLLY2) are supposed to correct for you missing a certain percentage, and distance to the animals etc, but that relies on you knowing what those uncertainties are.

I don't know how insect surveys are performed, but you have to understand that you're always trying to make sweeping assumption about "the whole of the US" based on very sparse sampling. Not to mention controlling for different environments. For example in the paper you cited, they try and control for a ton of stuff like habitat. I'm not an entomologist so I won't comment on the paper beyond that, but do be aware that "standard techniques" may well be something that we've done since the 60s and nobody questions it.