Let's see. Howzabout their chunk of the galaxy is very large? Also, relating more to the abramsverse, perhaps they lose huge quantities of vessels to more powerful intruders on a semi-regular basis.
I mean, 'the fleet' is occupied in the 09, so instead they send off all the rest of the available ships, which soon become jetsam.
Also, I don't get the idea that there is a shortage of starships in this version at all; the whole business of Pike saying Kirk could get his own ship in less than a decade makes it sound like there are PLENTY to go around, not like just 12 starships and a few science vessels.
Another thing: you're trying to reconcile a theoretical science notion about the ships with a longstanding cross-universe contrivance revolving around 'only ship in the ______.' The latter is a function (or disfunction) of plotting, the former a matter of credibility for some, and no matter at all to most.