The shared set there is basically just fat and exfat.
If Microsoft and Apple collaborated on a new filesystem, or even just supported it, then we might have a possible successor. However even with that, the millions of already shipped devices won't support it. This during the transition period of many years there will still need to be support for fat.
That keeps fat the lowest common denominator and everything supporting it.
The only way to get a universal standard is to have the community do it and have enough people use it that the big companies have to capitulate.
But as you pointed out, in a transitionary period there is still a need to support older devices and software. FOSS purists may also not approve of using exFAT in some situations, since the relevant patents have not yet expired, even if MS has released them to the OIN.
3rd parties can write drivers for Windows, you know. A small, read-only FAT partition on a USB stick or SD card could contain the installable drivers necessary to read/write the rest of the disk.
However, that's unnecessary. The best option for a universal file system is UDF. Windows, Mac, and Linux all have full read/write support.
Still, something similar to fuse might help with the licensing.
Do you know what happens when you insert a btrfs-formatted SD card or USB stick into a Windows or macOS machine? It tells you that the drive is unreadable and asks if you want to initialize it. If the user answers yes to that question, the system formats the drive and all of their data is lost.
With a BigFAT-formatted drive, the system will mount it no problem, the user will be able to browse the contents, and the only weird part is that their largest files are split into parts.
2. Switching to BTRFS would be a breaking change. BigFAT wouldn't be. You can still use the card in devices that do not support it, without needing to reformat. Those devices would just lose access to some files.