First, I want to thank you for the article. The ensuing discussion is some of the most interesting stuff on this forum. I have a couple comments I want to contribute to the discussion.
The answer is opportunity cost. Basically every time you buy a village, you've wasted at least $3 and a buy; you could have bought, if nothing else, silver. And most decks need silver early on to ramp up to buying 5s and 6s and eventually provinces.
This should probably be bolded or something, as it's the most important point in the article, and explains the exceptions people are mentioning. In the remodel into village/smithy or the mass peddler strategy, you *don't* need silver early on to ramp up to buying 5s and 6s.
In the "first game" set, the 5s are really weak (market and mine), so it's fine to live in the 3-4 range and go for village/smithy. In this case, the silver doesn't help that much, since you can get to 3-4 even without silver. So even though the village may do nothing for the first couple shuffles, it's not like the opportunity cost was really that great. Then the fact that you started buying villages early allows you to reach critical density of them sooner (around turn 8-9), at which point you can draw your whole deck to buy a gold or two, and then go green without ever needing silver. It's worth noting that while pure village/smithy is pretty bad as you mention, this type of strategy becomes much better in the presence of trashing, +buys, and/or gains, as highlighted in this example.
Similarly, silvers don't really help in peddler setups. Given that you have at least an extra buy, any cantrip is worth $2*(number of buys) for the purposes of buying peddlers, which is what you're going for anyway. Your goal is to get at least half of the peddlers by turn 7-8, at which point you'll have enough money from actions to go straight into gold and green without silver.
I still have a *very* hard time convincing myself to buy a village when I don't have enough terminals for it to be immediately useful, but there are definitely times when it should be considered -- specifically when the opportunity cost is actually quite low, and the potential future benefit is great.
And a note on walled village: The special aspect of walled village is that it's really not meant for these typical draw-your-whole-deck village/smithy-type strategies. (In these strategies, it's basically the same as a regular village.) The special thing they do is sit in your hand until you get a terminal collision, which they resolve. They are for when you have too many terminals and want to avoid collision. Here they work much better than regular villages, since you don't need to draw the village along with the collision -- you already have it in your hand, waiting.