Why don't you think it would follow the same cost curve as integrated circuits?
Yes. What's the cost of relocating software, or a movie, or an audio file? Very close to 0 (a few cents at most), and yet observe how much our current system prices each of those items. Capitalism, as practiced today, maximizes profits, not competition, I don't see that changing any time soon
You can see similar effects in hardware too, since even without self-replication there are already massive economies of scale. How much does it cost to get access to the output of most advanced chip fabrication technology on the planet? The answer is whatever the price of the latest flagship smartphone is.
Therein lies the problem with the assertion that prices will inevitably driven downwards: the price of a flagship phone is not driven by cost of making it - instead the OEMs select a price-point first and then work backwards from there. When was thr last time the price of a flagship smartphone decreased?
I'll tell you what I'd do with it.
I'd ask that genie for more wishes and have it start making copies.