Rival series do not "collaborate", they are rivals! GP2, FR3.5 and F2 are 3 rival businesses trying to compete against each other. Its not a "transition", for GP2 or FR3.5 to become F2 it would mean the FIA would need to buy them out. Not only will they not sell (can you see Bernie giving up a slice of his pie!), but the FIA couldnt afford them if they wanted too, they are quite sseriously in the red. So instead they are hoping that by making F2 far more appealing for an aspiring F1 driver it will cause one or both of GP2 and FR3.5 to wither and die.
Global motorsport is not a big happy family of chums all looking out for each other, it is a competitive market of rival series all fighting against each other to serve their own agenda.
In the 2nd tier single seater market there are 2 big players, GP2 and FR3.5. The FIA want in but have found they can't beat them (the first F2 failed), and they can't buy them out, so they are instead using their monopoly of the top tier single seater market as a lure to entice 2nd tier drivers into their own 2nd tier series, while hoping it makes some or all of the competition fail.
The FIA are not looking out for the wellbeing of global motorsport, they are looking out for themselves and themselves only, with potentially negative knock ons to global motorsport.