Hmm the 'exorbitant' military spending was a long term result of the great power rivalry with the USSR post WW2. The conflict was very much joined by both side with equal willingness. In that context NATO as such was hardly overreach. Also in general the US could sustain that spending. Neither the Korean war of the Vietnam war (the large scale military build up instituted by JFK) caused US debt to GDP ratios to do anything but decline. That's because the US used to tax itself.
Over that time day post war to 1980 the US could afford both types of spending.
If there was overreach it was started by Regan. Although not obviously and immediatly. After Vietnam and several years of not extravagant spending the US could afford the Reagan build up. After all if you not really fighting and expending war levels of ammo and equipment the cost was bearable. Problematically however Regan chose debt as his tool and not taxes (and pushed cut taxes in fact). That was deeply harmful. The FED seeing what amount double constant fiscal stimulus even during positive GDP growth kept rates high. Very negative impact on investments in the US vs oversees. Notably of course you can also see the internal investment get crowded out of the US budget.
https://fraser.stlouisfed.org/title/54/item/19029
page 6
https://fraser.stlouisfed.org/title/54/item/18994
https://fraser.stlouisfed.org/title/54/item/19032
page 7
As you can see defense spending did not really alter. Its juts other US spending (internal investments) was crowded out by debt payments and policy choice. Had the US maintained the 1970 tax code and had Regan say announced a surtax for his military plans no doubt the US budget would look much like the late 70s in the 80s.
But in any case when the cold war ended the Busch and Clinton did act responsibly so the was not persistent budgetary overreach.
Realistically the profound overreach was Bush. Fighting a endless war on terror and adding Iraq with debt and with his tax cut... well that was overreach but nothing to do with NATO or the budgets of it European members. Sad thing is if you net out the permanent Bush tax cuts, but keep just his temporary stimulus, keep the war in A -stan, but not Iraq and its quite likely the US would have been running a possible small surplus by his second term.