You can also avoid cat since you aren’t actually concatenating files (depending on file size this can be much faster):

while read -r url; do echo "download $url"; done < urls.txt

Tmux was purpose built for terminal multiplexing. You can assign session names for organizing and manipulating multiple instances. Send keys to and read output from detached sessions. It’s easy to script.

I’d recommend tmux for that particular use. Screen has a lot of extras that are interesting but don’t really follow the GNU mentality of “do one thing and do it well.”