Well “the price” might be totally different if there were no off-exchange orders. But I’m sort of being a devil’s advocate... I agree with your argument in practice since I don’t expect to see such open exchanges anytime soon
You won’t get a worse price than what the exchange says is the price, but that price Is a moving target; if all competitors could see all orders, the price would move. Idk if it makes a difference on average but it is a difference