Progress bars are something that have been researched and iterated on for decades now, and the overall sentiment is pretty clear – users like seeing numbers go from zero to a hundred while they wait. It doesn't matter if they aren't always accurate. Replacing them with a static "processing" message would absolutely increase user confusion and dissatisfaction with loading times. A while ago we put in a lot of engineer…
This seems like a surefire way to end up with a progress bar at 8675309%, or a progress bar that gets to 100% and then sits there waiting for reality to catch up. And I say this from experience, having seen both of these failure cases numerous times in the wild.
If users are frequently reporting that the application's getting stuck at a particular percent, then - to me at least - that's valuable information for whether I should consider doing some optimization to speed up whatever step in the process corresponds with that progress percentage, or to break down that step further into smaller steps to keep things moving, or both.