Installing windows - screws laterally into studs vs nailing flange?
You are probably correct that the nailing flange will hold the windows in place.
However, if there is ever a warranty claim, there's a very high likelihood that they'd deny it if you don't put the screws through face trim as they instruct. Heck, it's possible they'd try to deny the warranty because you've used screws (as I likely would) instead of nails through the nailing flange.
i.e. Failure to follow installation directions to the letter = failure to honor warranty.
Whether you choose to follow the instructions or take your chances on the warranty is your decision.