There is probably a good reason AJX/AJV want you to go home (scurry off, go anywhere, go away) upon completing duty. Employing foreigners to do anything in Japan is a very contentious issue.
And you only have to consider the bad wrap the Cathay pilots get in Hong Kong. I don't imagine that base in Tokyo for foreigners would be a very popular idea there.
The only two contracts offered by ANA that are commuting contracts are at AJV\AJX. All other contracts (ANK=737, A-net=Q 400, IBEX=CRJ's) are all residing contracts.
The reasons are very different than those you imply, it is a matter of "money" it is not social or political. It is not only the difference of salaries with our local counterparts but also the fact that there is no tax liability to the company from these employees since we don't reside in Japan