Your personal belief that Americans are exceptionally unlikely to steal your stuff is your belief to have. But I would still not leave my bike out for the Americans who do steal to take it and then have the other Americans who don't steal victim shame me "Oh, well why did you leave your bike out?"
It's just totally different man, culture is a hell of a drug. Maybe generally, if you're a lucky person, most people are honest, but A LOT aren't, and I'm not gonna be the one to drop my guard in America. I'll leave that to you and others.
I guess the people who stole my former startup's hardware prototypes and thousands of dollars of equipment didn't get the memo, nor did the professionals who broke into the bike lockers at a previous residence and stole thousands of dollars of bicycles.
Sorry to hear you have been a victim of crime, but are you sure the culprits were American?
Why blame a local when politicians always present an omnipotent and omnipresent foreign enemy?
The thieves could have been drug smuggling rapists that weren't stopped by a wall at the border. Or they could have been from Liverpool, where a sense of pride exists for being light fingered. I doubt they were true Scotsmen though.
I wouldn't and it has nothing to do with hand-wavy culture.
The reason I would not touch the unlocked bicycle is because I know it is registered with the police. If I got stopped on that bicycle and they looked up the frame number then I would have some explaining to do. Even if I claimed it was mine I could still be prosecuted for not registering 'the change of ownership' with the police. You could imagine the lying, language difficulties and the situation spiralling out of control to end up with time spent in the cells and a few million yen in fines. Could happen.
Note that in America a bicycle is a toy. It has only survived as a vehicle that can be used on the highway by fate, there have been plenty of efforts to fully ban the bicycle from the road and to denigrate it as a toy.
To extrapolate from the bicycle theft situation in Japan to assume that Japanese people are Not Like Us and therefore don't steal is wishful thinking. Personally I believe that Americans are exceptionally unlikely to steal your stuff. I am actually sure that if I did go on a round the world tour that I would find this matter of being honest to be a near universal human trait.