Consider a new coin called USD (or perhaps Digital Dollars or Electronic Dollars DDR or EDR). Perhaps a 2nd new coin called Physical Dollars (PDR or PDL). Some thought might be given to Pennies, Dimes, Nickels, Quarters, etc.
What does THAT do for you? On a 1 to 1 basis, you could track every single dollar created by the Fed. Each digital dollar would be identifiable and unique. An end to digital counterfeiting aka a bank or other entity creating an accounting entry that misrepresents the number of dollars in existence.
I think what you search is something like BitUSD or NuBit. They both hold the value of 1USD artificially.
And no, i don't see any government being interested in it. They want to print money when they need money.