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
It's true that a token doesn't need to be pegged, but without pegging, it will be just like any ordinary token (not a stablecoin). By the way, ETH isn't a stablecoin either.
Minting with burning money as "gas" isn't new; look at the BRC-20 tokens. They aren't stable.
What makes a token "stable" is its ability to maintain the same value. If the goal is to have 1 token = 1 USD, then it must be achieved by pegging or backing with real USD. In the short term, this can be managed with an algorithm or other mechanisms, similar to the fixed vs. floating exchange rate scenario in macroeconomics. However, in the long run, people have already learned from events like
Soros's actions and the 1997-98 crisis.