Epic has since confirmed to TechCrunch that both cross-platform play and progression on the Switch work with everything except the PS4. We've also asked Sony for its take.

It's not entirely shocking that Sony might put up barriers to playing on both the PS4 and the Switch, as it's clearly the dominant console maker and can use this to cement its position. However, this restriction may be more grating than most. The Switch version of Fortnite can offer portable gaming that a PS4 simply can't. Provided Sony is responsible, it's effectively dictating where you're allowed to play using your main account (assuming the iPhone version won't cut it), not just your choice of device. That may produce the opposite of Sony's intended effect by spurring Switch owners to either play on Nintendo's system instead of the PS4, or else to get an Xbox One for their living room sessions.