The Adepts Mechanicus does share tech. All STCs they find are given to Mars, and Mars then redistributes them to people they think can be trusted.
1. Nobody said they don't share tech at all, they just clearly don't share it enough.
2. Where is there copy of the original Vanquisher Cannon STC again? And why haven't they distributed it to a single Forge World even though the one other Forge World that had it lost it due to Orks in the 35th Millennium? Oh, that's right, they don't have it. They've got most of the Mechanicus STCs, but they don't have all of them.
There's a reason that not everyone is given them, and that's because not everyone can be trusted. There's a reason that the military doesn't tell everyone how to make nukes and F-22s. The Adeptus Mechanicus has a pretty good record of not releasing technology that causes problems
Nobody is saying that everybody should be given every STC. Again, the problem is that they are far too restrictive in who they give it to, which results in totally unnecessary losses of technology. It's utterly ridiculous that for a polity the size of the Imperium that is at war as frequently as it is that something as valuable as the Vanquisher Cannon would only be produced on a single Forge World.
Some technology has become lost as the Archeotech factories that produce them have been lost.
It's not just due to factories not working anymore. They lose actual STCs and other bits of valuable transferable knowledge.
You can't take away control of STCs from the Adeptus Mechanicus and let them keep their religion. They're a mystery cult that believes that STCs and technological knowledge in general is sacred and should be reserved for the initiated, with the higher mysteries restricted to the inner circles of the cult, because the common man can't be trusted with it. In 40K, they're essentially right.
The Mechanicus would still be the ones to actually use them. Nobody in the Administratum would actually know how they work. You don't need to know how to make a toaster to know what it does.
Has it been determined your society needs more toasters? If yes, look at the toaster STC's ratings. Value, low. Danger level if captured by enemies, low. Technical difficulty, low. Ok, send it on the next transport to Industrial World X and have the AdMech there get to work on building toaster factories for the masses.
Does your military need more Vanquisher Cannons? If yes, look at the STC's ratings. Value, very high. Danger level if captured by enemies, very high, Munitorum clearance required. Technical difficulty, high. Ok, can't send it just anywhere. Find a list of Forge Worlds with high enough ratings in security and expertise. Consult with Mechancius advisers over candidate list or whether it would be better to expand production on an existing world. If a new world is best, get Munitorum approval and send it to them under heavy guard. If production expansion is better, allocate resources to have an existing world that already has it build facilities to expand production. Either way, the local AdMech can handle the details of how they get to work.