I also don't see why the market would give any special value to this altcoin
This would be the key. If you could somehow make the currency attributes specific to that state then people would be encouraged to use it. Like, maybe it's a POS token where there is a rewarded amount given out to every citizen of the state every transaction or some sort of distribution based on property or something unique to that state (oil in Texas, Uranium in Utah, etc.).
The USD is a world reserve currency but it is being destroyed.
In order for an altcoin backed by a state to be valuable, it would need to have some attribute that other mediums of exchange do not have.
States could have their state specific altcoin backed by some natural resource, so in Texas, for example, might have one TXcoin be backed by 1/10 of a barrel of oil, but this would mean the altcoin's value would be based on the underlying commodity. States could also give some incentive to use their altcoin in financial transactions within their state, for example, a state could exempt transactions involving their altcoin from certain taxes, such as sales tax, but I would see little reason for the state to do this (what benefit would the state receive?).
As to your comment that the USD is being destroyed, I would note that other major currencies, such as the Euro, UK Pound, Yen, and Chinese Yuan are all seeing similar levels of government borrowing in each of their respective currencies. Based on this, I don't see the US dollar losing its status as a world reserve currency based on government spending/borrowing. The massive global government borrowing may result in global inflation, but we have seen historically elevated government borrowing levels for about a decade without excessive inflation; maybe there is a limit to this borrowing, I guess we will see.