The UNSC had been using nukes for the entire war, as they're practically the only thing that scratch Covenant ships. They were running low everywhere even before Reach.
The UNSC even at the height of the war doesn't issue nukes in large numbers. (If they had, it might have helped.) A destroyer or cruiser typically only has three to five Shivas aboard.
When you compare that to the figures for maximum warhead production now (Did you know we build over 1000 a year? Warheads are planned obselence and have to be replaced.), never mind what we
could do (the United States has the capacity to build over 100,000 warheads a year if it ever feels like it, and Russia something like twice that, nevermind if you get the rest of the world in on the Deus Ex Nukina defense.), it frankly seems the UNSC is just
really stupid.