Again... there is no rule that says one cannot trade off optimal gain staging for convenience or ease of mixing in a particular case.
If you feel it makes it easier on your board to do what you need to do and you're not concerned about the gain staging tradeoff, by all means, do what you feel works best for you. But as long as we are talking generally accepted best practice for gainstaging a conventional board, the section from the A&H manual and my posts and others describe that.
(With regard to your practical example, riding gain on a key vocal -- it's likely that that important vocal will, when the channel is properly gainstaged and the overall mix is developed, likely
be up near unity anyhow. If one needs more wiggle room, it may well be worth the tradeoff to tinker the input trim.)
Now, it may be worth pointing out to others not following closely, that what you're suggesting is
not the same as what the OP's instructor seems to be saying. If the OP is correct,
he seems to be suggesting that one should leave all one's output faders at unity and mix with trims. A substantially different approach to what either you or I put forth.
PS... with regard to unity gain -- unless I'm going going to my
board for a saturation effect (
far from likely), I treat unity as a target maximum. If, OTOH, someone is running a +6 dB signal
into the channel, then he
is going to be reducing the amount of usable throw on his slider since he's got to pull it down an extra 6 dB right from the word go. I know that others feel like they get more 'analog warmth' by hitting their boards hard. Maybe on their boards, they do. Every design and every situation is potentially different. My philosophy is this: I want my mixing device (real or virtual) to be clean, transparent, neutral and precise in control. I want my storage medium to be accurate/transparent. And then
I will shape the signal using tools specifically designed for that purpose.