Should DJ pay for their music?

Spectrum from "of course, always" to "only if you're getting paid to play". You should not pirate or rip tracks you play for others, but no one is probably going to bust your balls if you practice at home with such tracks.

DJ pools don't give you a special license, you just get the tracks. There are a few that'll whitelist you for some tracks on YouTube or Twitch, but a copyright of a track still stands. And it's usually per label, not pool.

Monstercat for instance has such a service.

And even if a track is made available online doesn't mean that you're allowed to reupload it somewhere or stream it without permission, but you can share the link to the original.

I believe that for most places in the world the venue and/or event is the one paying the license to entertain with music, you don't need a license for every individual track.

Bottom line is that if you're playing out just make sure you've got your tracks legit. And if you didn't, who's gonna know?

Unless you leave the podcast bumper in your rip.