You can use a screen, there is no problem with it, it can help make sure there is an air pocket and nothing is compacted at the bottom of the bowl and often makes the smoke cooler and easier. I think the idea that screens are kind of like training wheels is very apt description.
Protect? Nah I doubt they really offer any protection. I used to use screens alot more, but one reason I stopped using them as much is that there are little ends at the bottom that are sharp and will likely scratch, scrape, and damage a bowl. I would say as far as protection goes, they're more of a risk than a hedge, especially on old briar. One place I find them especially useful is for cob pipes where that gd stupid wooden stem is sticking out of the bottom of the bowl - but are otherwise excellent smokers.
Cleaning? You just grab them, put a little water on, and run a stiff brush across them. Honestly easier to clean than a stem or bowl.
Smoke quality? I think the smoke session quality is largely improved by a screen, despite what naysayers will tell you. I feel like I get the "down to white ash" thing happening with a screen much more consistently than without. You don't get the bowl goop, and the wet smoke as easily either. There are alot of things solved by a screen that traditionalists have just learned to tolerate or claim they are so talented and experienced at smoking that it never happens to them anyway. When people dump half a bowl of unburn tobacco and write it off as dottle, I think they're just using the strands as a screen and throwing away good stuff.
Screen hate? Pipe snobs shun them I think partly because it's one more fiddly thing they don't want to deal with, and because it's not traditional. Not dissimilar to filters. They're not wholly irrational reasons. You don't want to have to mess about with filters and screens, etc if you're out and about, for example.
Ultimately, they make them for a reason, lots of people use them for a reason. Sometimes you don't want to play Russian roulette with pipe packing and the screens usually give a solid consistent smoke.
Just my 2c