It can give a significant advantage, but it doesn't necessarily.
Sure, it lets you boost both offence and defence at the same time. And it removes the whole disarming worry.
But if all you want is as much firepower as you can get, it's actually worse. And if you don't have Refinements, it's strictly worse.
So there's still a reason to pick normal Channelling.
Equal Refresh Comparison:
Charlie
Channeling (No focus item slots, can take refinement for pyramid-less specializations), Refinement x5
Superb Lore, Great Discipline/Conviction
+5 Control Specialization, +5 Power Specialization
+9 Control
+9 Power
Chip
Channeling, Refinement x5
Superb Lore, Great Discipline/Conviction
Focus Item 1: +5 Offensive Control
Focus Item 2: +5 Offensive Power
Focus Item 3: +1 Defensive Control
Focus Item 4: +1 Defensive Power
+9 Offensive Control/Offensive Power
+5 Defensive Control/Defensive Power
How is it worse at all, at equal refresh, when you have the ability to take refinements? It's bad game design, because it's you sacrifice power now for power later, which causes imbalance at all levels of the game (at low level, you are unable to contribute as much, at high levels you're better than everyone else). Oh, and not only is a regular Channeler less powerful all around, but that power can be taken away with one or two actions (that would require fate points or perfect rolls for Chip in order to resist of Charlie tried them).
Granted, Evokers are balanced against this (as the +1 refresh gains them more elements, specialization, and foci, which slightly more than taking refinement twice could do). But their extra offensive power is subject to disarming (a disarm of their foci actually makes them worse than Charlie, and Charlie's better at offense than they are at defending against the disarm maneuver).
Elvira
Evocation, Refinement x4
Superb Lore, Great Discipline/Conviction
+3 Primary Control Specialization, +2 Primary Power Specialization, +1 Secondary Power Specialization
Focus Item 1: +4 Offensive Control Primary
Focus Item 2: +3 Offensive Control Secondary
+11 Offensive Control
+9 Offensive Power
+7 Defensive Control
+6 Defensive Power
So the channeler with spec's is arguably the most powerful of the three (although the Evoker is probably still the best in actual play rather than a head to head). At this refresh, you'd look stupid playing a regular channeler. Channeling is only viable when saving Refresh then.
So you're going to extrapolate from a single instance to "focused practitioners should be more powerful than generalists"? Doing so requires fallacious logic.
I'm not going to count pages for a rebuttal but Cowl makes Mort look like the scared one trick practitioner he is...even in his own specialty.
Beyond that, the books repeatedly call the WC wizards strong compared to others. Against that it makes one statement (that I can recall) about Mort being better than Harry at Mort's specialty. Don't think it compared him to a wizard who might have studied Ectomancy and related fields at all.
So no, I don't think it is necessarily true. As noted before, I think it's possible for a focused practitioner to be more powerful in her specialty than a given generalist wizard. I simply think that's a rare event, not a general rule of "should be more powerful in their focus".
This. I think an equally powerful (in game terms, equal refresh to Mort post GS) wizard who has studied Ectomancy would be just as capable, if not more powerful, as Mort.
Just like I don't think a gifted fire or force focused channeler would be more powerful than Harry or Luccio (depending on whether we're talking power or control) at using fire in combat. Possibly able to be more versatile with their fire due to the inability to use other elements, but not more powerful or better at controlling it.