Most of the one upmanship regarding appointments is between the 3 branches of the UK military, far outweighing the competition from overseas.
That is bolleaux, particularly in the OF3 / OF4 arena. The US have vast numbers of officers in these ranks performing jobs that would be carried out by OF2 / OF3 respectively by any of the single UK services. This totally skews the rank structure at any organisation the US are involved with, and is why so many UK OOA posts are filled with officers acting 1-up. It's almost become standard practice! As regards the more senior appointments, PN has it right - I should think about 50% of the alliance members are interested in little more than getting their 'fair share' of the command opportunities.
It's easy to scoff at the multinational HQs, but what happens when something like Libya kicks off? Our relative lack of engagement in the NATO command chain caused us difficulties throughout. Obviously this was worked on as the campaign progressed but it would have been much better had we been fully involved in strategic decision-making at the start.
Isn't it a truism of military operations that many of your key assets will sit comparitively idle, waiting for their big opportunity to be used? That applies as much to senior officers as tanks. If the seniors are maxed-out in peacetime, then the advent of war could cause decision-making to grind to a halt. Perhaps that might be a good thing!