It's really as simple as: if you want to be an asset that has considerable value compared to US Dollars -- either go it alone (that is without US Dollar investment) or follow the same rules (CSAM bars, AML, KYC and sanctions) as USD.
Not sure which path is best right now. But that's only because I generally follow USD regulations as currently crafted. However, remember I was introduced to bitcoin because of anti-poker legislation in the US.
Eventually, yes we won't care about USD convertibility.