Just hang around Maxios; take a Hegemony Commission and kill Tri-Tach and Pirates all day long. If you're not making money, you're doing it wrong.
The problem with the campaign mechanic is largely fixable:
1. The drop rate on Normal difficulty is absurd, to the point where you pretty much must plan to Pursue and get all of the cargo ships to make money (but it works just fine then) and it just doesn't make much sense to hit non-cargo fleets. Easy difficulty, things are fine without bothering.
2. The freighter fleets aren't carrying sensible cargoes that are actually worth money, other than Tri-Tach. They may be traveling to X Market that wants Y commodity, but that's not they're carrying. This is a major oversight, because it largely breaks piracy as a thing and makes being a privateer artificially difficult.
3. It's still oriented towards one-ship-kill as a strat, because of the way CR works and how it's scaled; if the solo-killers cost a lot more supplies to field, we'd all be using fleets, other than die-hards.
4. Early game remains the place where things are painful. Once you've gotten a second Frigate with a leveled Captain, the difficulty begins dropping very fast.
The difficulty ramp in general remains the opposite of what it should be; leveled Captains have largely helped the player overcome the CR system, rather than producing a difficult late-game threat.
That said, I've found that mixed fleets of Destroyers and Frigates can be very very effective, simply because they can jump multiple fleets in a very short time period, win all Pursuits and because then you get killing power and cargo enough to make steady income.
In my current test game, I've amassed well north of 3 million credits in two days of playing; I've killed about a million in Bounties and I took a Tri-Tach Commission to boost earnings a bit, but largely it's been about cashing in cargo. I never had to use anything past Destroyers in this game; a single Medusa can kill practically anything with a little support.
And yes, you really can build fleets that largely don't take Hull damage, ever. PD is a thing; perhaps you're simply not optimizing correctly? For example, a two-Flak Enforcer with a trio of Shepherds is remarkably good at nullifying every missile-boat and fighter in existence, while continuing to kill Frigates and most Destroyers like it's going out of style, for a very low cost in Supplies. The biggest thing here is that, if you want that to happen, expect to spend time grinding Captains and Dismissing Captains that get sub-optimal tree choices; a Captain that doesn't get Power Grid Modulation early is not worth investing in, because it's a life-or-death thing for AI ships, as is getting Gunnery Implants and Helmsmanship at 10 and Evasive Action at 5, imo.