Tech mining colonies to get the final blueprints that the player is missing. Once the vast or extensive ruins are mined out, you convert the shut down the tech mining and switch it over to whatever industry is available for the world. An Alpha core on tech mining along with a story point increases yields by 50% if I remember correctly, so vast ruins are always pretty useful to mine.
My gameplay experience is that installing an alpha core in Tech-mining is a complete waste of resources; whether or not you also spend story points to improve the industry and regardless of what level of ruins you're working with, it does not appear to meaningfully improve the chances of getting things that you actually want or noticeably extend the useful life of the industry, and a 50% increase in the amount of garbage produced by Tech-mining is closer to what I'd call a penalty than a benefit.
Also, unless perhaps you're setting up way out in the boonies and refusing to use any items, a few well-developed colonies can easily cover your operating costs and then some - if I recall correctly, Dorus alone can net something like sixty to eighty thousand credits per month, depending on how much of its import demand can be met within faction, from Commerce, Light Industry, Fuel Production, and Refining even without anything boosting production, and Ogygia will do about as much with the same setup. Why bother keeping (former) Tech-mining colonies for income when you already have more money than you're ever really going to need?
Size three AI worlds are a good stopgap money printer
They're an
awful stopgap money printer because if you leave them going too long you're not going to be able to recover the alpha core you installed as a governor, which makes abandoning them once you no longer want them problematic, and on top of that a size-3 mining colony with decent resources and accessibility can pull in fifteen or twenty thousand without any items invested or probably more than double that with an Autonomous Mantle Bore. Additionally, while it can vary quite a bit from game to game, alpha cores are quite often not something you have in the early part of the game when you might actually
want something that could reasonably be described as a "stopgap" money printer, especially if you're setting up your 'stopgap money printer' before exploring a nontrivial fraction of the sector.
Lastly, pirates no longer raid player colonies unless they reach enough hostile activity,
A Patrol HQ likely isn't going to do anything meaningful to the sorts of fleets that pirates generally send out to raid colonies, especially if the hostile activity meter actually gets high; the point of putting one in the system is to do something about shipping raids, because shipping losses can cripple colonial income and it doesn't actually take that much to kill a lot of the smaller fry that might go after trade fleets. It'll also passively contest pirate control over any satellites in the system, which means less baby-sitting.
Which means the only thing you have to manage is the Hegemonies AI inspections, which can be easily bought off every couple years.
Pathers can be bought off every couple years, too, or shut up permanently if you give them the bomb, and there's a significantly larger benefit to sticking a couple alpha cores on a major colony with a base income of over a hundred thousand than on several minor colonies with a base income of maybe a fifth that much.
Also, a major colonized system can stand a pretty good chance of fighting off an AI inspection fleet (or, really, any other expeditionary force) without player intervention, so if you really want to take a hands-off approach to colony management putting the cores on the big worlds is a much better way to go.
Kanta's wrath is impossible to remove, even by destroying Kanta's den. So, completing the story causes 2 additional HA to be tacked on forever.
Angering Kanta may be the best and fastest way to get through that part of the storyline, but if I recall correctly it's not the only way to complete it.
Also, so what if Kanta's mad? Blowing up an inconvenient pirate base or two every now and then is hardly a problem for the sort of fleet you ought to have by the end of the storyline or with well-developed colonies, and even at 5 stability base pirate interest plus Kanta's wrath is only just over the passive hostile activity reduction of a military base on a size-6 colony.