How fertile is the Vale?

You may have already covered this, but I wonder exactly how fertile is the Vale? According to the wiki: “The Vale proper is a tranquil land of wide rivers, and hundreds of lakes. Wheat, corn, barley, pumpkins, and fruit grow in its fertile soil.”

By all accounts the Vale seems to be more bountiful than the North and probably the Westerlands. Yet for some reason the Vale can only muster about 30,000 or more soldiers at its peak, which is on par with the North. 

I find this a bit peculiar because though the Vale proper cannot compete with the Reach and Riverlands in producing as much food (according to your estimates the Riverlands could boast an army of 80,000 at its full potential), surely it should still be able to sustain a larger population than the North and therefore be able to raise more troops.

I’ve discussed this here. The issue you’re missing here is one of size; the Vale proper is quite fertile (“a tranquil land of rich black soil…even in Highgarden the pumpkins were no larger nor the fruit any sweeter than here”), but it’s not very large compared to other regions of Westeros (”Though the Vale itself is famously fertile, it is small compared to the domains of other kings (and even some great lords), and the Mountains of the Moon are bleak, stony, and inhospitable.”) 

Take a look at the map: 

That blue circle is the Vale proper; the rest of the Vale is all mountains. That little triangle is just about the size of the Trident, far smaller than the Riverlands or the Westerlands as a whole, let alone the huge expanses of the North or the Reach. So while the Vale is quite fertile on a per-acre basis, and far more so than the North, the North has so much more land than the Vale that it evens out.

(Incidentally, I said the Riverlands at full strength ought to be able to raise 40,000, not 80,000 men).