Somebody else might be able to give a more technical answer, but here is how I understand it. The different metals certainly have an influence, but I believe the final human adjustment plays the larger role.
The machine made reeds are usually just riveted onto the plates with very little further processing. As long as it makes the correct sound then its done. With the various degrees of human processing the reeds are adjusted to perform better. You could say that each individual reed is special as a result of whatever manufacturing reasons and minute physical differences. When these are merely stuck onto the plates they are not optimised to their own strengths. When they are adjusted by hand each reed is made to perform optimal based on whatever is optimal for that specific reed.
There is a discussion, with lots of photos, on a German music forum about reeds (
specific example where basically the same Hohner Artiste reeds are used in a Hohner Atlantic IV De Luxe and a Hohner Morino VIM, but the difference is in how the reeds are finished. In the latter case the hand finishing was done with much more care. From this you could say that any reed has a certain potential (although limited by the quality of the materials used) and to unlock the full potential you need to put in human effort. That is how some some people can turn a bulk, factory made box into something a little better by adding that human touch.
I think a possible analogy would be the kind of teaching a student receives in a group class context versus one-on-one tutoring catering for his exact needs.
It should also be noted that the difference between handmade and machine made isnt that the former has the reed carved by hand from a lump of metal. The initial cut is still done by a machine. Its what comes after that where the hand part comes in.
As for why machines cannot be made to do this automatically, I suppose it comes down to our own subjective feelings. When all the reeds are done to highest hand standards everything needs to fit together as a whole. The closest a machine would come is getting perfect pitch and the most optimal performance but in an isolated environment, i.e. the reed by itself. But the overall character might end up being machine perfect.