As a player-
For convenience yes It's would be awesome to have progress saved and be able to carry from PC, PS4, and Xbox.
It seems all it would honestly require is a portion of the coding that EA has been working on FOR the rumored crossplay capabilities to accomplish.
profits side - it makes sense to keep them seperate and require additional purchases. Let's not forget at the end of the day everyone's trying to make more money while spend less.
Maybe a compromise could be reached and let 1 legendary skin per character and each individual weapon be carried over.
stats can be managed by OVERALL, Season, and Platform. (Can be done with the drop down menu selections)
*Battle pass should always be purchased on the individual platform.
All in all it seems maybe this exact reason is why cross play is still not released???