Exactly. When my stove was installed 6 years ago, my installer told me that I should remove the screen because it would clog up. And it did, a little, but only because I had to use rather moist wood and hadn't quite got the hang of the stove. After the first year, I have had absolutely no buildup at all on my screen, even a little. It's there for a purpose, and other opinions notwithstanding, if you do things right, there should be no problem.
I will say, I'm not experienced with cat stoves and they do burn cooler, so maybe that could be an exception sometimes, but otherwise, if you are getting a buildup on the screen, it's probably due to some kind of operational issue IMO.
It's a controversial subject that comes up frequently here, but my opinion is to leave the screen alone and figure out why it's clogging. It really shouldn't.