It turns out that although we're #1 in shots/game, we're ranked 17th in the league in SOG%. The average team in the league has 36.5% of shots on goal; we have 33.6%. If we were able to shoot as accurately as an average team, we'd have an extra 0.5 shots on goal per game (3.5 extra shots on goal for the season). (This would only be good for ~1 extra goal so far this season... not much.) Our offense does take a lot of shots, as people have pointed out, but not particularly good shots... this ends up in an overall average offense (we're 10th in goals scored per game).
I was frustrated that "nobody besides Villa shoots", just because he shoots so much more (5.7 shots/game) than anyone else on the team (Mendoza is second with 2.3 shots/game). But I was wrong - they're taking shots. So what's with Villa? It's not because nobody else shoots... maybe he's a greedy player, or maybe he just doesn't trust his teammates to take good shots...
In terms of SOG, we're probably better off with Villa shooting. If you look at shot accuracy for the team, Villa, even with all his shots, has average accuracy (they average player has ~37 SOG%, Villa has 38%).
It's Mendoza that has been the problem... 14 shots, 0 on goal. Probably because he usually shoots from midfield. Bravo is 0 for 5. Tony Taylor is 1 for 7. (These are just to get a shot on goal, not even to score.) Shelton just doesn't shoot (as we've seen, he doesn't seem to know what to do with the ball once he dribbles it down to the final 3rd).