Bounty hunting becomes mostly unviable, very fast.
There's certainly a difficulty spike in the mid-game as you're forced to get in bed with a single faction (+ the independents, for what they're worth), decreasing the number of available bounties, and the bounty fleets ramp up in difficulty faster than you're able to acquire stronger ships. Mid-game battles were pure torture where the outcome depended entirely on whether some of my ships decided to suicide into an enemy deathball, and savescumming was the only way to success.
However, it doesn't stay unviable forever. Once I was able to acquire a Paragon by sucking up to the TT, the game has become incredibly easy. This one battleship is able to wipe out anything that comes at it. I run just the one Paragon for the actual battles, an Aurora, a Medusa, and a Wolf for chasing down escaping bounties, a couple of small freighters, and a tanker. My operating costs are basically nil (~2.5 supplies per day when at full CR), and because the Paragon barely ever takes any damage I don't have to pay out the ass for repairs either. I barely ever need to buy supplies or fuel, since big bounty fleets leave behind a lot in salvage, and I'm currently sitting on 2M credits, a spare Paragon, a bunch of other cool ships, and a huge stockpile of weapons that I bought just because. The game is very boring, though, as there are long stretches where I just sit and wait for a bounty to pop up that I can actually do.
But is this repeatable? Or every consequent investigation is going to behave as the 3rd? (which I suspect is the case)
Nope. The officials will start rejecting your bribes, leaving you no option to prevent conviction.
As long as your relation with a faction is not vengeful, you can briefly build your rep back up to inhospitable by performing their bounties 'pro bono'; you won't get paid but you'll still get the relationship increase. However, once you're back to inhospitable, a new investigation will be launched that will bump you back down to hostile.