Double posting to add some examples directly related to your bug report. My current game I have nothing but basic armour, spent ages researching any tech I can think of that might conceivably link back into the armour tree but am not having any luck. Am about 3-4 tiers ahead in most stuff I can imagine could be locking it out. The screenshot I posted above is an example from slightly earlier on in my game. (You can't see it, but in the middle to the left I only have Armor Plating tech from the start and nothing else.)
I've done some testing, starting new games with random tech but revealed at start and have noticed it can have some pretty esoteric links to later armour tech, though not entirely unrelated. Some of the more extreme examples (probably not 100% accurate due to memory) were Assault Marines linking backwards to tier 2 or 3 armour, reinforced construction which was locking out any armour until the same tier of about 4 and Resilient Armour pods doing the same but for the highest tiers.
You can get very awkwardly locked behind some convoluted prerequisites your don't even know are required until you stumble upon it by chance, or get completely orphaned techs for some pretty vital stuff (like armour). I'm starting to think I might be in this situation:

- MeatShield.jpg (32.19 KiB) Viewed 1080 times
And example of having
No access to Carriers or Battleships, which seems pretty brutal:

- CapitalPunishment.jpg (160.37 KiB) Viewed 1080 times
A pretty harsh one, only the first upgrade to mining; also an example of some somewhat unpredictable prerequisites. I think High power receptors needed Electromagnetic Defences, about 20 techs further up the screen. You can also see that not only are High Power extractors required for Automated Module Manufacturing (which isn't totally insane, but seems a bit too arbitrary) but in this case the linked techs are combined orphans:

- UnderminingPower.jpg (176.34 KiB) Viewed 1080 times
Just to cap it off, as 4 images seem to be the limit, this also seems pretty brutal. Locked out of engine tech halfway through:

- GoingNowhereFast.jpg (164.35 KiB) Viewed 1080 times
If this is ostensibly working as intended and these are just examples of very bad luck with the RNG (I didn't have to start that many games to get these examples), can I suggest that there are certain limits on how bad it can get.
From what I have seen, it is impossible for a random tech start to lock you out of, or even change, the links for any of the colonization or diplomacy techs; I can see why that might be the case but seems odd that, as shown above, capital ships and basic armour weren't given some guarantees as well.