Super extreme nitpick, it's listed at $9.00 on Apple's store:

http://www.apple.com/shop/product/MMX62AM/A/lightning-to-35-...

I must say, I'm a bit shocked at the price. I wouldn't have expected Apple to sell a paperclip for under $19. Their Lightning to USB cable, which seems like it must be strictly simpler than this adapter (no DAC!) costs $19.

I don't think this cable contains a DAC. I would imagine they use some pins of the Lightning connector to transport Analog audio. They still need a DAC for the speaker and such.

How small are DACs? I was surprised that the new Lightning earbuds basically look identical to the current ones besides the jack. Do they definitely have a DAC built in or is it still in the phone body?

Looks like they're pretty small. They're single chips, and small ones at that. Here's a datasheet for one I found at random:

http://www.ti.com/lit/ds/symlink/pcm1754-q1.pdf

That lists the size as about 6x5x2mm. Should fit comfortably within a lightning connector.

Consider that the new wireless earbuds have a DAC in each earbud, plus a full Bluetooth radio, all squeezed in there.

You can always buy a new iPhone 7 for another free adapter.

Joking aside, I think most people won't notice as the new EarPods connect to the Lightning. That is what I mostly see people with iPhones around having.