It's actually pretty lousy idea, because in practice it's exactly what we already have in normal banking system, where the "bank-USD crypto", that is, the numbers in your bank accounts, are already backed 1:1 by actual government USD, with government regulations backing the companies and the exchange rate.
If you can freely exchange cryptocoins to USD, there's absolutely no reason to ever consider a stablecoin, unless your goal is to evade money laundering, KYC, etc regulations, hence Tether.