Well this study hasn't definitively isolated pesticides as a cause, but it did successfully eliminate a large number of alternative explanations, making agricultural pesticides a likely contributor. Whether consumer pesticides contribute is also an open question, but it makes a lot of sense. They're designed to kill these insects, so widespread application is a reasonable hypothesis for the decline in insect populations. It's functionally habitat loss, which is well established as a cause of population decline in other animal populations. The theory especially makes sense when you consider the particular areas covered by this study.
The authors looked at flying insect populations in various protected areas in Germany, where pesticides are not applied directly and thus are not impacting populations locally. But since those populations are so mobile, the surrounding areas' pesticide levels certainly could be. Many of Germany's protected areas are surrounded by developed land, doubly so for those covered in this study. Most of the data collection occurred in Nordrhein-Westfalen, which is landlocked and surrounded by one of the most heavily industrialized and intensively farmed regions in the world. The rest took place in Brandenburg, which is similar. They're also not wide open plains like much of the American agricultural heartland, where insects can blow through more rapidly.
So, maybe we would see less decline in America, where there are much wider swathes of undeveloped land. That wouldn't disprove the pesticide hypothesis, it could merely indicate that the blocks of pesticide-free land in Germany are too small to form a sustainable habitat for flying insects. That would mean we need to create larger blocks of pesticide free land.
Maybe that doesn't mean we need to stop using pesticides, but does mean we need to reconsider the scope of their use. Deprioritizing non-essential uses such as lawn maintenance, for example.