Can the U.S. Open With an Air-based Strategy in Allies and Axis?
The US can't afford to waste money (and time) building planes
The trap the Allies fall into when considering an airpower-based strategy for the United States is to evaluate the strategy on its own merits instead of by comparing it to the alternative strategies.
The question points out that a large bomber force can do more IPCs in damage than it would expect in AA-gun losses--which is all true. However, it neglects three important considerations:

It takes too long to implement. The US can only afford two planes a turn and starts with one bomber. This means a 6-bomber fleet takes three turns to build and it isn't available until the Combat Phase of turn 4. Furthermore, it will take an average of 15 IPCs per turn to maintain this force in the face of AA losses--about half the US economic output.
If all the US has been doing until turn 4 is build bombers then the game is probably already over (a fait accompli if not an actual economic victory). Also remember that because one bomber a turn is needed just to maintain the force at 6, the US can only afford 2 transports OR 5 infantry per turn afterwards. Granted, a smaller force can attack in the prior turns, but the net IPC swing is too small to hurt Germany, and any AA hits set back the strategy by a half turn.

The strategy can collapse in the face of bad rolls. One turn of good AA rolling by Germany, or a multi-bomber run that only does a few IPCs of total damage, and this strategy is defeated. In contrast, the typical shuck-shuck strategy can't really be defeated by bad luck. The naval force the US and UK can set up by the end of turn 2 can't be attacked by Germany without decimating their air force, and deterrence of German aggression is the entire point of shuttling a mass of Allied infantry into Europe.
Good players tend to shy from luck-based strategies, believing that they will eventually win a game decided by skill but could lose one decided by luck.

The opportunity cost of building fighters is too high. This point has some overlap with the first, but it is a distinct argument. The key metric is not how many IPCs a bomber force can destroy compared to how much it costs to maintain. Strategies have to be compared against each other. The goal is not to bleed Germany for more IPCs than the US has to spend, it's to use the US IPCs to their greatest effect. Bombers are just not as useful as a fleet of five or six transports dropping off 10 infantry a turn in Finland, France, or Algeria.


Lastly, to quickly discuss the fighter-heavy variant that was also proposed.
Sure, a stack of fighters is pretty dominating on defense, but a stack of infantry four times as high is more dominating: they will do more damage on average, are cheaper to replace, and can actually occupy territory if necessary. They are slightly less mobile, but the battle lines in Europe move slowly anyway (when they move at all), and the consequences are much less if some get caught alone in a territory because the UK and Russia decided to bail on a lost cause just before Germany's turn.
So given how much less effective a plane-based strategy is than the shuck-shuck, I would not choose it. Even if some good tech rolls made it occasionally a winner, lots of times the tech won't work out.
I'll take the eventual sure-thing over a long-shot any day.