The issue is there are a plethora of execution things to look at with the offense, although compared to how bad things were in McCarthy's last two years many have improved. OL assignments and player performance I'd say has improved a little, but I think this next offseason we'll have to draft a pair of new OTs.
But the 40 second clock management definitely ties into execution, and the offense as a whole has formed bad habits with it. It doesn't rest on Rodgers head alone, but how often does he try to hurry things up in the huddle? As the QB and the longest tenured player on offense, he usually directs traffic and of course the snap count.
I'd say even more so than taking unnecessary timeouts or penalties, it potentially allows the defense to catch their breath when the offense is slowing up with the play snapping. Not to mention I've seen this junk happen on series where the running game could have potentially put the nail in the coffin on the game. When Jones and Williams are on a roll, you're slowing things down too much by failing to keep track of the play clock and then taking DOG or burning timeouts.
Fans are right to be upset about this faulty approach.