Giving all of those abilities out would not only make Specialist a little stronger than non-Specialist, it would also still force the Specialist (if he was not also an omnicrafter) to obtain refined materials off of the board. Someone who specializes in Weaver, for example, should get all the other 21 15, 37, 50 cross class skills - but to make most things, he would still need to buy leathers, grade 1 dissolvents, nuggets, etc. off of the board.

Remember - the point of Specializations is to allow someone to take one craft up, without ever touching the rest, and still compete. To compete, anything that can be made HQ must be HQ'able. That pretty much requires the cross class skills. Oh, it's possible, with heavy RNG, to do it with the Specialist actions - but not reliably, which means, not in a manner that allows the Specialist to compete.

The *perk* to leveling up any other crafting class would be the ability to, y'know, actually make that class' stuff.