That's literally the basis of the Apple lawsuit. Apple booted Fortnite because they tried to ecnourage players to bypass paying on the App Store.
Here is straight up an example of Epic undercutting iOS and Android. This type of revenue loss is what Sony was concerned about by allowing cross-progression, hence the deal. Now Epic could encourage people to go off and use the Epic store but they risk paying up if the ratios shift. So they either have to keep the ratio inline or ensure that revenue on other platforms exceeds the loss.
Epic certainly has pricing flexibility in their own store unless they want to sign a deal like the one you suggested and there is no evidence they have and in my opinion it would be extremely foolish. I work in marketing and price is a huge component. To give up the ability to flex prices on your own store would be a huge restriction. Hence why I am not surprised they chose Sony's plan instead of agreeing to strict price parity.