Something must be wrong when the worst shooter in the league takes as many shots as your All Star. Against the Heat Dwight took 10 shots, Big Baby 10, Nelson 11, Von Wafer 9, Q Rich 9. Right now none of those players are considered "solid role players" in this league, you wouldn't get much value if you wanted to trade them. So why would you give this below average players as many shots as your AllStar? Letting Big Baby take as many shots as Howard would be as dumb as choosing Jeryl Sasser over Tracy Mc Grady to attempt a winning shot. Oh wait we've already done that.
So Howard is arguably our best player, everyone and his brother wants to get him, let's use him! Dwight taking 10 shots a game is not an exception but the rule. I pulled out this stats from last season*: Dwight played 78 games, and only in 29 of those games he took 15 or more shots. How is he supposed to score 30 a game (as an Allstar is supposed to do from time to time) if the doesn't shoot more? Yes, he does get fouled a lot, but even including the fouls he doesn't get enough attempts.
While Howard attempted 15 or more shots only 29 times, last season Lebron James did it 68 times, the same number as Derrick Rose. Ok, they are perimeter players, they get more touches, blah. So let's see how are the bigs doing: Paul Gasol also beats Dwight attempting 15 or more shots 33 times, Zach Randolph did it 45 times, even Brook Lopez, yeah Brook Lopez, did it 56 times. So yeah, you can be big and still shoot a lot.
I guess now you'll say: "but all those players have more range than Dwight, it's hard to set him up in the post". Fine, that's true. Besides Dwight there are no Allstar Centers without range in the NBA right now. So I had to compare him with the last great Center without range I can remember: Shaq. Yes, he is a HOF, and played under different zone rules during his prime. So let's try to be fair and check his last big usage season, where he was old, had limited mobility and we can assume he was no better offensive player than what Dwight is today. Miami, 2004/05 season Shaq was 32, played 73 games as second fiddler of Wade and still got at least 15 shots in 40 of those games. He averaged 11.1 FT attempts per game, while Howard averaged 11.2 last season, so FTs are not a factor. You can tell that Shaq got more shots opportunities than Dwight, even with Wade being the 1st scoring option. Also, that season .530 of Shaq made FGs where assited compared to .532 of Howard FGs, so I don't think that playing along a superstar like Wade was such a big factor in creating FG attemps. Shaq was playing under Stan Van Gundy system, under the same rules, being old, battling injuries, and still got his shots.
If a 32 year old Shaquille O'Neal could do it, so can Dwight. And he should. I don't know if it's his fault, the coach or his teammates. But if you have an Allstar in your team, you better use it. Whatever it takes, just make it happen.
* This is a weird season, with weird schedule, so for statical purposes I think you'll get more accurate data from the previous one, also you get a bigger sample size.