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?
Could be rare items are fixed and not effected by the bonus, it could be rare items are affected by the bonus. Who knows, I almost always get something useful from doing this however, typically one colony item, a few blueprints although that depends on how many I have, and some AI cores.
I always set up out in the boonies as that's really the only place you find perfect systems. Depending on the run, my main colonies all located in the same system use at max 1 colony item so as to not attract Pather attention. In such runs I also typically have multiple high commands within the same system to ensure I don't need to bother fighting expeditions. When all is said and done in such runs, I'm making typically 200,000 - 300,000 a month. Which when taking officers, crew, and ship resources into account, is just a little more than what I need per month. With a handful of size 3 worlds, I can push that up to 500,000 easily.
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.
By the time I've decided to set up a colony, I've explored a good chunk of the sector, and typically have around 10 Alpha cores. If I'm going for a no babysitting run, as mentioned above, I'm not ever going to use the cores on my main colony, and it's unlikely my fleet will need them. So that leaves size three worlds as the one place they are useful. The stop gap is to help fund my main colony development. Of course, I could just resort to piracy to fund my colonies, but don't because well I don't feel like it.
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.
Shipping raids typically don't occur due to HA being low for small systems, especially when you have one massive system drawing all the attention. You don't have to babysit the coms as the colony will remain over 5 stability. If there's no coms in the system a colony gets -1 stability, if it's in the system but not under faction control +0, and if it's under faction control +1/+2 depending on com type. TLDR, there's no babysitting for size three AI worlds besides dealing with the Heg.
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.
Yes, but in the scenario where you use AI cores, you always have to pay off the Heg, you don't always have to pay of the Pathers if you set things up right. Likewise for RP reasons, paying off the Heg is okay, but paying off Pathers is a bad idea, giving them a planet killer is a terrible idea.
Unless you steal the Heg's Pristine Nanoforge, or have multiple extreme heat worlds with a high command plus a Cryoarithmetic Engine, they will eventually reach a strength where your colonies can't handle them. I haven't seen it this version, because I always steal their nanoforge, but in past versions the most extreme fleet I've seen from them is 5 very strong fleets.
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.
Time, effort, I'm lazy, I want to seal club larger and larger Ordos, and finally leaving pirate stations alive increases profits thanks to the core worlds getting hit with a -50% accessibility. Which typically only decreases their market share but lets them still buy everything the need.