This is silly idea, a stablecoin that has no collateral is not stable coin, its shit coin.
if your contract receives ETH and decides to give ERC20 token in exchange to the USD value of ETH received, and later burns it which honestly doesn't make sense at all

. This simply means you're just burning your money, the ERC20 that is minted from that activity will have zero value, nobody gonna buy it as it is deemed valueless since the ETH which can be used as collateral just got burned.
when you spend ETH for the token you have intention to get something in exchange of ETH with real value, and this "something" really does have a value for you cause you spent real money for that
So the token doesnt need to be pegged to anything the same way like ETH doesnt need to be pegged to anything.
Look at this token not as at regular token with collateral - but as at a product you buy
Things doesn't work that way, exchanging ETH to some random ERC20 doesn't make that ERC20 get valued the same as the ETH that got burnt, instead its just gonna have whatever value that ERC20 is packaged with such as the underlying dapps that utilizes that token or just gonna be another shitty valueless token.
using the same logic, those ICO that raised ETH in exchange for their token will have their token retain intrinsic value that ETH is having but the reality isn't really like that right?
when you burn ETH, this simply means you are burning the
ETH and its
Value. the ones that gonna benefit is the other ETH holder since the supply of ETH decreases so the value of their ETH increases.