Unfortunately, it's not a matter of "should." Professional sports teams make a LOT of money, so they can afford to pay whatever price is necessary to have the best team available.
If medical personnel were paid the same amounts as athletes, only a very few people would be able to afford medical care.
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Football is HUGELY popular and drives in enormous revenues for itself. This results in players making a lot of money. Are military personnel underpaid? I don't know. The two things, military pay and NFL pay are two different topics and not related. Remember that the military gets paid from your pocket so if you want them to make more, be prepared to pay more taxes.