The $1 valuation strikes me as way more arbitrary than $4k. What features mean that it should be near USD parity? It should either be above or below the USD based on >>insert valuation technique here<<. But why should it land near $1-2? Why shouldn't it be $0.003 or $30.00?

If it should somehow land on parity with fiat currency then maybe it should be a weighted mean of the global currencies but $1-2 seems incredibly arbitrary.