Yes. I don't know as much if they are out of F-4 drones as much as it is just more cost effective to use a newer aircraft that costs less to maintain. They fly those QF-4's a lot manned, and believe it or not, they do things like maintenance test flights after mx, just like you would for normal aircraft. The majority of the time, they are not shot down, so they incur a cost just like any other airplane. When I went through WSEP/Combat Archer, my Sparrow shot missed the drone on purpose to save it. If I recall correctly, for our entire det, only 1 F-4 was downed, and that was for a TD&E type of shot, where most are just for NCEA/live training requirements for aircrew. That said, it was pretty cool to watch my buddy shoot the thing down, and watch it spin down to sea in a ball of fire after he had speared the left wing off.
As for the F-16, people probably forget, but the Viper is a pretty old airplane now.....those early block jets have been in the desert for a while now, or are flying with "Navy" or "Marines" on the side. There are plenty to go around for target duty, while still maintaining the fleet Block 30-60 Vipers on the front line for many years to come.