The real reason is that modern defenses are now built to smother the pure winger on the flanks. You've got defensive fullbacks who are tanks, midfielders who drop back quickly, and nobody's leaving space for a guy who just runs in a straight line. So yeah, false wingers create defensive confusion like the second guy said, but it's bigger than that: it's mostly that you gain offensive flexibility and you can play between the lines instead of battling the fullbacks every 90 minutes.
Plus, clubs are looking to control midfield. If you put a classic winger who contributes nothing to the press and collective play, you've already lost two or three guys dropping back. Today's forwards have to take part in winning the ball back, create inside passes, combine with the fullbacks in more complex patterns. It's clearly more demanding mentally and physically, but that's also what makes teams win the ball earlier and play with more density.