I think something like that might be necessary. I probably wouldn't want to invest in a store that only took bitcoin. At this point anyway...
This is would not be a "store" in the traditional sense, it is a business that would permit financial anonymity of the investors and founders.
Such "Open Business" can't be implemented in current, existing business, only for new one.
And not for a physical business, only knowledge, software, services, or "under radar" ones, at least until government does not embrace Bitcoin and such accounting practices.
Bitpay break any anonymity, and hide financial operation (which happens off chain) from the eyes of the investors, thus breaking the open accountability of the founder. (Thanks to the published PaymentKey)
The goal is to allow anonymity of both, founder and investors, but allowing trust despite of it by having the internal books of the business open to every investors. (And retrievable from the blockchain)
Only bitcoin payments would permit to keep the anonymity of the founder, even if the book, and accountability is irrefutable and public thanks to the public "PaymentKey".
All back and forth in currency would break anonymity but also hide operations from CC holders (investors).
This is not meant for everyday business and physical store. And not meant for black market.
But as a way to incentivize funding of an entrepreneurial project by bypassing any financial institution or institutional barrier.
Let's be clear : Such "open business" would be a big legal problem, because normal business require banking account, and books in currencies.
But I expect legislation to change to accommodate it when they would not be able to stop such business from flourishing. (thanks to backed-in anonymity of investors and founder)
Maybe a good first way to try is out would probably be a bitcoin based gambling site. Where investors can invest their money and take out their profits at will without having to trust the site operator like they currently do. Would that be possible?