Below is the very careful wording from the blurb, and there is no suggestion of cross progression amalgamation, just that you can play with friends on the other platforms. If you change platform situation remains the same as now.
I can see where this may be a issue currently with the black market in accounts, etc. But if when the move is made to cross play I can see no reason why your one account could not then be used on multiple platforms.
But this might have its difficulties too. As an example my son uses pc, as we linked his account onto my xbox ages ago (its not used much as no progression saving), so how could he then log on on to the xbox and keep progression?
Bit disapointing but understandable.
"CROSSPLAY IS COMING TO APEX LEGENDS
Ready to take on the world? Hopefully your friends on other platforms are really as good as they claim to be. This fall you’ll be able to squad up no matter what platform your friends prefer - Xbox One, PlayStation 4, Switch, or on PC via Origin and Steam."