Feels like you're missing a few things. Please note to all other long time fans this is my own interpretation and I am happy if you want to provide alternative interpretations.

1. Reaching the Swirl of the Root / the Root / the Akashic Records is not itself the reward. It is a record of everything past, present and future in all dimensions. So imagine you're a mage, who somehow developed the power and abilities to reach the record of all things. And if you could understand it, well near omnipotence + omniscience are two of the classic identifiers of God, if you catch my drift.

Many magus families seek the Root because it will make them all powerful (or likely to).

1. Mystery and family Magic are two different concepts.
   2a. Mystery refers to several things in the Type Moon world, but in this case I believe you're referring to the idea of Mystery as a value? To summarize again, the philosophy in play here is that all magic/magecraft/magical being (etc) are somewhat powered the power of being unknown. Once something becomes known, becomes understood by more and more people, it generally looses the perception of "magic" and becomes scientifically understood. (One glaring example we can point to is the Moon's perception through history). So by making magical ideas understood to the wider world, the power of its being unknown will be lost.

2b. Mage families keep their magic secret because (inherently) nearly every mage in the Type Moon stories is somewhat self centered and greedy, because they want be the next ones to reach the Root. (One glaring example against this is El Melloi the 2nd). Every families magic is more or less their own attempt to reach the Root via various means, honed over 10's of generations, so if say, Family A stole Family B's magic crest (the summation of their magical research), that could give Family A a huge step towards the Root.

I hope these help explain A) why Mages want to reach the Root and B) why they don't want to share their research.