Eh maybe not that far. If a parent is a Wind Mage then his kid is likely to become one. If he's a Thunder Mage then his kid would most likely master that over let's say Fire Magic.

We can also say that mages need their tomes/staves to channel their magic energy and all.

Hm. What if magic in the world is fearfully respected? Like many people might be happy to have a Mage on their side but others might be extremely wary.