The problem with taking a true neutral as the Axis is that you open up Spain as a landing point for American forces. This means that continental battles with the US are only transport turn away.
Secondly, USSR now has a stronger incentive to mess with Japanese affairs, because while the declaration of war gives Japan 12 IPC (alpha 2+), it also allows them to swing down into Mongolia and pick up the troops there.
Thirdly, if Scandanvia is at all threatened, Sweden becomes an attractive point of attack for the allies – pick up a few extra guys and deny a German NO.
Finally, it’s worth mentioning that the Allies can pick up a small army in South America. It’s kind of removed from the fight, but send some transports down there with tanks, and you can fill up on infantry before heading to Africa.