No, Channeling doesn't permit taking Refinement for specialization. It can only get you more focused item slots (or enchanted item slots if you trade them in).
I thought we'd agreed to hang those rules.
By the numbers, a FP can be better than a wizard who doesn't pay any attention to that field (at least with Evocation, Thaumaturgy grants you access to all kinds of ritual magic) but can never be better than a wizard whose bonuses are placed in that field. If I've understood the rules correctly, granted.
Like I said, the rules are assuming that a focused practitioner is not just a wizard who is specialized in one field, but someone with less overall magic, so if they were to spread it out, it would too little overall to actually do any magic, that's why they are specialized like that. Wizards just have a larger reservoir of magic to draw from, so even if they do a sloppy spell, there's more than enough to make it happen. But even if you keep to the specialization rules, you can have a lot of bonuses on items, which will be more than enough in most cases.
And then, of course, there are aspects. I touched on it before, but maybe let's take an example. We have a wizard who is specialized in fire magic, a warden maybe, with 3 points in fire specializations and maybe 2 points in items, so overall, not a newbie. And then we've got a fire dancer, with 6 points in items, just to make them equal in refresh spent.
Now when it comes to slinging around fire, the warden is probably going to be better, granted. That's his job, after all. But lets look at more subtle usages. Like going into a burning building and getting out a group of kids. The warden would have to use brute force to will the fire away, and I would have the fire resist him at a skill of 5 or 6. But the fire dancer is so used to playing with the flames, that for him, this is a whole lot easier, maybe a roll of 3 or 4. Instead of forcing the fire away, he dances with the flames, lulls them in, calms them down, etc., and so he creates a path for the kids to escape.
But ultimately, if you want to create a character like the one you are looking for, you'll have to do a bit of work on tweaking things, because the focused practitioner from Your Story just isn't the same as the kind of character you have in mind. You could look at the custom power list, especially the "incite effect" section, it might be the power you're looking for.