If we consider for a moment the way things used to be, there could have been an English draft for English teams and so on for other leagues.
At the European level teams would play with whatever they have because it wouldn't make sense to have a different team just for the CL.
Of course I don't entirely understand how the draft works either Teams can also get foreign players through the draft somehow.
If you try to accomodate the rule changes since the Bosman act, and lower divisions it becomes more complicated. But there are people who get paid and could figure it out.
Just imagine even the Scottish league. If the talent was spread out between all the teams instead of just two. The level may drop but it really doesn't matter because it's all relative anyway. I could get some guys from the street and call them Brazil and people will ooh and ah every touch.

This may seem far fetched but all it takes is for one league to implement it. Like the way the 'Russian rule' was implemented in European basketball ( which you may not be aware of )