How do you think would the the price in USD of such stablecoin always stay close to 1.00?
Stablecoins are backed by collateral assets that are usually controlled to help manage the price of the stablecoin itself. Any entity or organization that holds these stablecoins (if it is a centralized platform) or those who hold the collateral that is used to back up stablecoins usually try to control the supply and demand so the price stays as close to $1 at all times.
You have explained in details the mechanism that governs the issuance and supply of stable coins in response to their demand. This is very complex task to maintain the value of stable coins such as DAI, USDT or USDC close to 1 US dollar. Which is very crucial for the stability of the market, if this peg is broken, it can cause significant disruptions in the market. We have witnessed collapse of UST token of LUNA foundation rapidly losing its value to the extent of 99% when its peg was broken.