I'm not saying Overlord was a bad idea, I would have wanted it. But would it not be better if we also invaded Yulglosvia and Greece? And then move into Hungry or Bulgria. Would it not be better for these countries not to be communist?
There are a finite number of landing craft, personnel and material available. The Balkans were, at best, a sideshow. Logistically the area is a nightmare. The concern of politics post war took a back seat to actually winning the war, but a Balkans offensive would do anything but improve the post war world overall. Rather than have Hungary under Soviet control, you wind up with all of Germany and probably France inside the Soviet sphere.
The attack into France was the only one that made logistical sense. The supply line is short, you have plenty of air support available and its located on land, not a carrier that needs to withdraw on a regular basis to refuel and is vulnerable to the lucky enemy sub or bomber pilot, and you have to cross under 100 miles of water which allows you to directly deploy LCM from UK ports.
The reason that Dragoon went as well as it did was that the Heer was already badly disorganized due to losses and pressure from Normandy.
Italy is a REALLY bad idea. The terrain get WORSE for the attacker as you move further up the Peninsula. There is very little space to maneuver, and the vastly superior logistical and CAS capacities of the WAllies. It is worth remembering that the German positions in Northern Italy didn't fall until May 2, 1945.