Well, I don't think that mundane weapons should have an attack power of 1, unless its designed as such.
Training should be longer for more complex weapons, but the weapons' effectiveness should remain the same.
As stated in my post, the numbers given are only examples (placeholders, if you would) and have nothing to do with what I believe the actual strength of a given weapon should be. Anyway, why not separate weapon type and training time? That way, you would be best off giving your untrained cannon fodder conscripts easy-to-learn crossbows, while leaving the potentially more powerful (but harder to use) longbows to troops that you are willing to spend training time on. However, if you foresee the need for longbowmen in the future, but lack the funds to train them enough right now, you could still recruit them with little to no training and simply hope that they will gain enough experience to use the weapons to their full potential.
As for if it makes sense or not; picture it like this:
A crossbow is powerful enough to penetrate armour at close distance, but is rather inaccurate and takes time to reload. It is relatively easy to use, requiring little upper-body strength to reload (if you're using a crank) and you only have to point it at whomever you want dead. However, even though training with it will make you more proficient with it, you are still restricted by its very design. Even a veteran soldier won't make a (medieval) crossbow accurate or quick to reload, because those weaknesses are inherent in the weapons design.
A longbow, on the other hand, is hard to master, but is tremendously powerful once you have done so. In this weapon, the weakest part is most often in the soldier (ie. if you changed the soldier to a stronger and more experienced one, he could draw quicker, but if you instead changed the bow to a larger one, you wouldn't get any better results).
I do not know what the flaws are in this system (please point them out to me, so that I can refine my idea), even though they are there (there are always flaws in every unit and weapon design system), but I would say that the strength is that it ensures that certain weapons are best left to troops that you are ready to spend large amount of wealth and many turns to train, and other weapons best for conscript, while at the same time making sure that even the conscripts get better at handling their weapons as they gain experience.