In an article published by TheVerge, Sony CEO Kenichiro Yoshida, made it clear that everyone asking for cross-play with "Fortnite" to shut up - it's never going to happen. To paraphrase without taking the whole quote from Verge: Yoshida said they've decided to keep their doors locked based on user experience.
So, again, that's basically telling everyone who wants cross-play to "STFU. You have PlayStation 4. PlayStation 4 is the best place to play 'Fortnite' and you will love it."
Yes, yes, we all love Sony's PS4. The console is unmatched thanks to exclusives such as "Bloodborne," the soon-ish "The Last of Us 2," "God of War," and the upcoming "Spider-Man" game. If you want to play "Fortnite" you do it on the PS4 or you're out of the club, kid.
This isn't even about money, it seems. This is about pride. A pissing contest that is, probably to Sony's eyes, they have won, since Microsoft and Nintendo have started cuddling each other with "Fortnite." If you've accessed your "Fortnite" account from the Nintendo Switch to the PS4, you can literally never go back as Sony holds onto your account like a creepy old man about to flash you.
It's really hard to say how cross-play can really affect the overall experience. It's not as if you can play with over a hundred people on a single session. But it'd be great though, if you could play in the PS4 while in home and then use the Switch while on-the-go.
Nah, Sony don't swing that way. We love you Sony, but, as Andy Warhol would say, "One's company, two's a crowd, and three's a party."