Or walled gardens that his parent company maintains.
You can install games on your PC from any source, and there are over a half-dozen good games distributors you can choose to shop from or sell on. And if none of them work, you can also just buy directly from the developer themselves.
If Apple allowed multiple app stores and sideloading on iOS, but pulled in a few exclusives (ie, Apple Arcade) and banned Fortnite from its official store, that would be equivalent to what Epic is doing on the PC with the Epic Store.
And that is exactly what Epic wants Apple to do -- it's a completely consistent position for them to take.
It is perfectly fine for Epic to focus on suing the companies that are causing them the most trouble right now. Given their relative size compared to these companies, it would be stupid for them to take on everyone at once. They don't have the resources to sue every major player in the entire games industry.
"out of the goodness of their heart" is also a silly way to characterize this positively or negatively: They want a chance to compete with Apple by offering lower costs in exchange for not offering the same feature set as Apple, just like how the EGS on Windows does not offer the same feature set as Steam. They believe developers will pick them due to the lower cut, but that's something the market would decide. Right now the market can't decide, because Apple has decided to prohibit competition.
Incidentally Epic made a public promise that if Apple lowered the cut, Apple Pay users would get the same Fortnite discount that people paying directly get.
They are just PC spoiled.