That would get gamed immediately and we'd be in the same spot. Allow price differences for problem customers that require more attention and airlines will say that why they change prices basedcon certain factors.
Ah, but this is worst in industries where resale is not possible. For example, flights, digital games, and rideshare. Of course one has the option to just not fly, buy games, or use Uber, but this limits a lot of convenience and function in a modern society. This is why I think targeted regulation is not such a bad thing - provided, as you explain, that the reason for the price discrimination is not because the customer actually costs the business more.