That's a common method in the DR. My buddy spent some time there and when he got back that's the only way we'd drink it. Still have one but don't use it...I'm going to break it out! When we were in CR recently we learned that they like to make their coffee with a chorreador which is a cotton sieve and stand. The sad irony about CR coffee as well as that from Guatemala (I spent some time there and met a crazy Australian roasting coffee in a small building with an ancient brass roaster that took up the whole room) is that the locals all drink Nescafe. All the good coffee is exported to the states and the locals either don't have access to or can't afford the good stuff. Was really depressing.
Chorreador:
Size of roaster manned by cracked-out Australian in Guatemala:

I went back to this pic I randomly found on the net as the guy in gray actually looked like the Australian I had met. Turns out, there's a really cool story behind it:
Coffee roaster ‘piece of history’ in Yacolt - The Columbian
And here is the coffee he sells...available on Amazon:
https://www.amazon.com/s?k=pull+caff...f=nb_sb_noss_1