I always thought the weave/loom stuff was just meant to indicate that their culture is based on creche children. We could almost do the same thing now, and when that concept was introduced decades ago it was high sci-fi. They're not really even sexual as adults anymore. they just take some blood, brew up a new batch of gallifrembryoes, toss them in "the loom" on the off chance it will imbue some of them with timey-wimey resistance powers and allow them to regenerate, turn on the centrifuge to separate out the downsies, and then raise/educate whatever makes it through the process in a camp/farm Brave New World style.
It's a highly ordered, rigid, aristocratic, authoritarian culture without carrying many of the negative implications that usually come with those words. But it's also a culture which allows for individualism and even requires it to exist -- hence requiring the children to look into the abyss at some point and the "Mad" Doctor who is able to save the day when High Lord Commander Rassilon is fresh out of ideas. And oops -- The Master. Well, no system is perfect. I don't know that any of them have ever directly stolen from Brave New World, I wouldn't accuse them of it at all, but it has always struck me as a very similar theme/idea. Because it's just a strong idea in the first place.
I mean it's Dr. Who. It's not going to make a lot of sense. But that makes enough sense. The first time we ever saw them in action the Time Lords were more like officers in Her Majesties Royal Navy than anything.