Secondaries that give satisfaction - it's difficult to recommend because they are all much less forgiving than primaries. Over the last couple years I have settled into Kuva T Stubbas as the most reliable. You must mod to each faction, mod to reduce recoil, be a headshot hog, and have a decent Riven.
Same logic for Ten. Cycron, Prisma Gremlins, Ten. Plinx, and some others.
Also your specific usage needs to have a narrow focus within your whole build. Yes you can main a secondary all the way through SP, but enjoyment will drop unless you are ok with being much more strategic in your engagements. Some people say secondaries are only good for priming enemies but that is simplistic. They are situational. Big maps are better for stubbas and plinx, cycron and gremlins love packs of enemies.
So to your point above to use it as main damage, find some fun synergies with unairu armor shield strip, the vacuum arcane from little duck, and cycron. Or be cooler than the Loki mains of 2016 and run pillage gyre and plinx. Laugh maniacally as you orange crit headshots and profit. Secondaries aren't mains for everyone, they are mains for mad scientists... 😆