I can imagine many potential conflicts of interest in this two-wiki arrangement, most concerning is the possibility that the scope of Wikimedia could be restricted in order to drive users towards the for-profit.
This is not a hypothetical. Contrary to the "Imagine a world in which every single person on the planet is given free access to the sum of all human knowledge. That's what we're doing." tenet, massive amounts of information has been actively moved off Wikipedia to for-profit wikis -- I'm talking of course about such things as Star Wars, Star Trek, Pokémon etc.