In the grand scheme it's a somewhat small one, but there is an incentive system in place to try out different weapons in the form of the Turf War vibe meter. It's a bit like in the first game, where wins and losses would give and take away points, but unlike S1 where higher vibe gives you a small per-rotation cash bonus from Judd, hitting vibe milestones at +5, +10, and +15 with any weapon will give bonus experience. This is also how you build up the little colored flags that show up on every weapon, so you can keep track of how good of a winning streak you've had with every weapon in your catalog. Not earth-shattering, but it's something.
As for Salmon Run, the points that are doled out at the end are given based on how many power eggs and golden eggs you collect, so you are getting something for that stuff, with score x pay grade giving you points toward your bonuses, redeemed at the front counter. If you get lucky with your bonuses you can score some pretty nice stuff compared to spending that equivalent of time in the general multiplayer.