They already do this for the opening and closing auctions. You can have a market-on-close order or limit-on-close order for example. The market on close orders are guaranteed to fill. The limit orders are filled using price-time priority, so best prices submitted earliest fill first, after the market price orders.

I guess it is possible that there are remaining marketable orders that never fill because of an imbalance one way or the other, but I doubt that ever happens in practice.