Always thought a 'foreign legion' type setup would benefit here. If people are passionate about certain regions of the world, or courses, they should be able to opt into it. Would create competition across national armed forces, too.

Would be interesting to see which theatres would be most attractive to recruits, and which military operations would be off the table through nobody believing in them. Could potentially mitigate the idea of 'signing up to die for corporate interests' if you had agency in what you're potentially fighting for.