Longbows were cheap in a couple of ways. They were made of common materials, and while they required specialized skills to make, they weren't any more difficult to make than other weapons of the era. The expensive parts
Have to do with time. When the wood is selected after the tree is cut, it has to spend something like 3-5 years seasoning before it's ready to make a bow out of. Then once it's made, you can really only expect it to last 15-20 years before it rots/decomposes enough that it's not a top grade war weapon anymore. In active use (ie if actually issued to archers at war as opposed to being carefully out away after training) they might only last 1-3 years. So you have two problems:
You can't make them 'on demand' however many you have at the start of the war is about all you will have, as new production will only probably keep up with replacements for ones used up in the field. And when the war is over you can't save them for next time, because they won't last that long. This ties in with the need for constant practice by the archers. The English rules requiring constant bow practice existed for two reasons; to get the archers practiced ( of course) but also to ensure that more bows were continually being made.
In wartime many methods were tried to get more bowstaves faster. None of them really worked. You either continually made them in army sized quantities, or you weren't going to have any long bowmen when a war popped up.
Crossbows and guns are different. They can be made on demand, and store better too.