From what I can tell Epic has two (three, depending on how you count) main arguments against Google. The first is what you mentioned - that they _do_ have the option of sideloading an app like Fortnite. The problem being that they lose out on a massive market because they don't want to use Google's IAPs. This is made worse by the fact that Android gives "scary" warnings when trying to install an app from an untrusted source - which is arguably a good thing for safety/security, but at the same time questionable when Google also benefits from it.

The other issue is that Google actively makes it harder for an alternative storefront to operate on Android by forcing OEMs to only include the Play Store (though I think OEM's own stores might also be acceptable? not sure) if they want Google Play Services (which most apps require). Which means Epic can't go out and make a deal with an OEM to add the Epic Store (or possibly even just a single app like Fortnite that doesn't use Google's IAPs, not sure) to an Android device because said OEM would have to drop Google Play Services.

And they can't just tell you to download the store - there are limitations that you cannot bypass without being a system app (i.e. something preinstalled). The most notable one for a store being that it can't auto-update other applications.