Creating a stablecoin without backing or an algorithm is tricky. In your idea, people send ETH to a smart contract, which checks ETH's USD value, gives tokens equal to that value, and burns the ETH. The challenge is keeping the token's price at $1.00.
Since there's no collataral, the price depends on market demand and supply, which can be unpredictable. If demand drops, so does the price. if demand spikes, the price could go over $1.00. Without a stabilizing mechanism, it's hard to keep it steady at $1.00, making this kind of stablecoin risky and likely to fluctuate a lot.