In reality, tickets sold on connecting routes have to be priced quite a bit below tickets that are non-stop in order to garner traffic. Would passengers be able to differentiate between a non-stop and connect carrier for a specific O&D and take price into consideration when deciding which carrier to fly with? For this to work, non-stop carriers would have to be allowed to take a price-premium against connect carriers and not lose all market share.
Source: This is what I do for a living.