This is actually how most of the European equities markets start and end the trading day. During the auction period, anyone can submit an order at a given size

This is actually how most of the European equities markets start and end the trading day. During the auction period, anyone can submit an order at a given size at price. When the auction ends, the exchange matches at the price that maximizes the number of shares traded. The rest of the trading day operates in what is referred to as a "continuous auction" where orders are matched continuously based on price/time priority.