For what? Using USPS is not compulsory. Having an APO/FPO is not a protected class. There are already restrictions on what can be sent to an APO (to include things that are illegal in the host country, like Bahrain). And logistics processing outside of your companies "normal" flow is not compulsory just to appease a US grunt.
There are plenty of companies that don't send to APOs and they continue to exist without doing so just fine.