Besides the cool thematic reasons, are there any mechanical benefits for choosing an FP over a Wizard?
The extra refresh you don't have to spend.
That said, I do want to address why it's that way thematically in-universe. The idea is that magic isn't discrete blocks but rather a broad field of knowledge whose various facets blend into each other. Knowing how to use Water can make you better at using Fire, because you understand how the fluid aspects of fire act. Knowing how to set Veils can make you better at Wards, because now you understand the parts of Wards that act like Veils a little better.
A "specialist" isn't someone who knows only about his little area of specialization and no other. That's like saying that, for example, a specialist in Middle Ages history is someone who knows nothing about other historical periods. That's not how it works. First you get a broad education on all historical fields, then you go learn more about the specific field that interests you. Ignorance doesn't make you superior. A true Specialist is someone who understands the broad area of knowledge and then goes on to focus intently on the particular area that interests him.
So for example, the true specialist Ectomancer would be someone who has Thaumaturgy (so he's learned how Wards and Summoning work in general) and has taken three Refinements in being better at Ectomancy. He is going to be much more awesome than some guy who never got a proper education to begin with and is just sort of winging it on Ectomancy and nothing else.