I don't know, but I might guess that they chose png because screenshots are not high resolution (a 1080p screen is ~2 Mpixels) and so they didn't think heavy, lossy compression was necessary, and maybe they thought there was some use case for which you might want an exact reproduction (which jpeg, being lossy, won't in general provide).
Personally I only take a couple of screenshots a year, and most of those are only stored temporarily, so they are a negligible contribution to my storage use.
I'd check what both WiFi and BT are used for in any particular camera: a direct WiFi connection between camera and phone can probably also be used for transfers. Also check whether any particular software is needed on the phone (I'd expect "yes" in many if not all cases - my own camera is too old to support this, but as a Nikon user I'm pretty certain my next camera will require Nikon's "snapbridge" app for such things to work.