Chips being cheap makes sense at the lithography / wafer level because sure, you can stamp out thousands of them at once. But once you need to dice them up, bond wires to them, and package them... how on earth do you do that so efficiently that each chip can be sold for fractions of a cent?
Today, it's cheaper mostly because of flip chips and Wafer Level Chip Scale Packaging (WLCSP). You build the bond pads as a normal litho step, and use a dielectric that's non-wettable between them. Then you can just use a mask to produce a grid of solder balls in the right places, drop the chip on them and put it in an oven. When the solder melts, the chip will self-align on it, so long as it's not too far off. It's uncanny to see it move.
The bonding machines are crazy. Definitely look it up on YouTube, the machine puts down bond wires super fast.
The other part of it is sheer scale. Once you start making thousands or millions of something, economies of scale drive the costs way down
This does not match my experience, although I imagine it's true in some parts of the industry. I've seen bare dice usually delivered as KGDs (known good dice -- tested at the individual level, not just the wafer level). These used to be shipped in waffle packs, but I've more recently seen blue tape used for delivery, and going straight into pick-and-place.