>The system I described only has one unit of account, Bitcoin. It doesn't matter whether they're on-chain or "virtual", they're both Bitcoin, and are worth the exact same amount.

Ofc it matters because those bitcoins cannot be used as part of the bitcoin network they aren't bitcoins at point at best they are some weirdly defined bitcoin option. As long as I won't be able to spend those bitcoins as bitcoins and as long as it's not enforced by the network itself this won't really be fractional reserve banking, or at least not what people consider FRB since CAR is an important part of it.

>You have misunderstood fractional reserve banking. Banks are not allowed to give out more money than they have received in deposits. Here's Wikipedia:

I think you misunderstood my point I should've been perhaps more clear about how money generation through fractional reserves works currently and how multipliers on deposits work: https://en.wikipedia.org/wiki/Money_creation I assumed based on the topic we've discussed so far "creating new bitcoins" it was a given state.