And again, this is before we get to the problem of “the government lets you do this.”
Cryptocurrencies are currently considered securities under US law. You can't just pop unrealized securities into existence when a prospective investor asks you for them: it's akin to naked shorting. That's why the stock market has "market makers," i.e. firms that provide low-latency settlement of securities in exchange for a small part of the spread.
I can't find any evidence online that any reputable exchange is using its underlying reserves to cover multiple in-kind balances. If you have links to exchanges actually doing this, both I and the SEC would love to see them.
Edit: I'm struggling to even find links to people discussing this hypothetically online. I found this one on a wiki[1], where it's discussed in the abstract. And I found another thought piece from the Atlanta Fed[2]. But no indicator that any current above-board reserve is currently doing this.
[1]: https://en.bitcoin.it/wiki/Fractional_Reserve_Banking_and_Bi...
[2]: https://www.atlantafed.org/cenfis/publications/notesfromthev...
I used the US as an example; what you're describing is illegal on every single major international exchange[1]. And as far as banking licenses go: the FDIC won't touch Gemini's actual non-third-party-custodial depository products with a ten foot pole, and they're about as clean as a cryptocurrency firm can be.
If you want cryptocurrencies to "succeed" in some nebulous sense, it would be good to get a start on the "not just good for crime" part of the equation. This isn't it.
[1]: https://en.wikipedia.org/wiki/Naked_short_selling#Regulation...
I don’t know of any exchange that offers a deposit account that’s dollar-denominated but backed by cryptocurrency. I can think of lots of reasons for that, FDIC regulations being the least of them. But again, even that wouldn’t make the number of bitcoins in circulation increase: it would be an unstable (and illegal) financial fiction.