I use them, even in my colored stuff. I tend to convert them to flat colors tho (as opposed to halftone) since what I use are mostly patterns for fabric or to use for a design of something.
Tho I use halftones a lot, cuz I think they look cool.
Screentones I love but they can be tricky to use. Like oh sure they look great NOW but when I have to make the page smaller is the screentone going to look terrible then?
Tho I do use screentones for stuff like backgrounds, which you can see here:
The stars are a simple screentone pattern I made up in Manga Studio 4. But as you can see I made it pretty big with the stars far apart.
Anyway, I love manga screentones, I wish I could utilize them better, and I envy those that can use them well. But I also love halftones for a kinda throwback to old school comics.
That said I learned a trick for doing everything in flat colors then faking a screentone look. Just grab a mangacap, it’ll probably have that “compressed” look like a lot of manga scans tend to have, find a good screentone texture you like, crop that tone, then make a pattern of it in Photoshop. It adds a little texture to it without having to do all the work of screentones. There’s a more detailed tutorial on it somewhere.
But basically yes I like them. I’m not sure if they’re falling out of favor or anything, but I do like them.