The only progression is cosmetics. You'll likely run into more players if you go to the world events. Look for big clouds shaped like a skull or ships. Only one at a time I believe and will be there until a crew clears it. Sometimes it'll feel like an empty server and others you'll get a lot of PVP action.

I haven't played for a while and don't know if safer seas affected high seas players since there were a lot of players mad about the safer seas being added. I always assumed it was players who liked hitting soft PVP targets.

If you really want to have random PVP encounters become an emissary for one of the factions other than reapers. I'd suggest gold hoarders. Any level 5 reaper emissary will be able to see your ship on the map while flying the emissary flag. You'll become bait for them to hunt down.

Also there's the hourglass to do PVP.