I disagree with your economic assessment about the fundamental price of BitUSD. USD in your privileged financial entity pays 0% in BitUSD pays 5% which should more than make up for regulatory issues.
This says that it is redeemable but that implies it is a debt instrument, instead I would say that it always has the purchasing power of about 1 USD
Well, the answer to the OP question is trivial - you peg the price to USD by convincing market participants that bitUSD is a 1:1 substitute for USD.
I am not saying it is redeemable or has the legal power of a debt instrument - only that it should be fundamentally valued as such. "Fundamental" value is nowhere the same as "market" value, which makes most of this a moot point similar to "academic" vs. "engineering" discussions.
In practice, we can overcome these issues for market participants, e.g., through widespread adoption to make costs negligible, or a 5% dividend, or a good PR campaign. Even a dividend paid in crypto would suffer the same conversion / tax losses to fiat, and each individual would subjectively value it differently due to future uncertainties, but I doubt most market participants would consider or price that in to the equation.
Although the intent is to get them as close as possible, bitUSD value cannot be fundamentally equal to USD value. One is a unit of measure in a wealth system, the other is a unit of measure in a debt system. A person cannot expect wealth systems to completely replace debt systems. You cannot completely eliminate either, and you need to consider system interfaces.
For cryptocurrency systems in general, fundamental value is based on cashing out to legal tender - i.e., exiting the system. This is evident in current differences in btc prices across exchanges / currencies, which can be fundamentally attributed to the cost / time / ease to market participants of cashing out if market effects such as liquidity and information imbalances are neglected.
I hope that bitshares and crypto markets in general will not have to consider this - either crypto will become so widely used between individuals that you do not need legal tender in day-to-day activities, or so widely accepted that cost of converting to legal tender can be ignored in day-to-day activities. But currently, we have no financial institutions that will even convert btc to legal tender - exchanges convert and only act as approved payment processors divisions of banks to impose KYC regulations. Fiat exchanges must absorb the cost of maintaining fiat reserves / debt funding to cover any runs on cashing out, e.g. if price rises suddenly. Crypto-only exchanges ignore this wealth-debt system interface, and pass this issue on to others to address.
Ideally, crypto and bitshares would result in people using USD only when it has to be used - whenever governments say it has to be used, which from legal tender laws would be for payments to governments - taxes. Right now, this is not how USD is valued - it is considered a substitute for wealth as well as debt, but the growth of crypto systems will only clarify these value distinctions.
A bitUSD will only have the purchasing power of 1 USD if someone else accepts it as a substitute. If someone accepts bitUSD as a 1:1 substitute, that is only saying they will have no obligations to convert any of it to USD legal tender for taxes / government payments. If they do have obligations to convert any, they would add a premium to cover the cost necessary to do so. This cost will ultimately depend on regulations and fees from fiat exchanges to cover operating costs and reserve risks.
I like to build castles in the air but, without a solid foundation in the real world, I will never be able to move in. I have to consider that some portion of cryptocurrencies will need to be converted to real-world fiat, and I need to conservatively assume that is the limiting factor for an assessment of fundamental, objective, ex-crypto-system value of a bitUSD.
I would propose the two questions below as thought experiments:
1) How does I3 expect a person to be able to pay taxes using bitUSD?
2) Assume you own a store that sells physical silver. As the store owner, you are ultimately responsible for meeting any regulatory, reporting, sales tax, etc requirements.
Customer A walks in with 1,000 bitUSD in his account. Customer B walks in with 1,000 USD in his account. Both can swipe a card, push a button, etc and transfer their account balance to yours with the same ease and cost. Both expect to receive more silver than the other, and will not buy if they are not offered more than the other.
Which customer will leave your store with physical silver?