Originally Posted by
JellyPooga
This. Right here. This is my disconnect.
Ok, run with the arithmetic analogy. When you're faced with a problem that you can't solve easily, you count on your fingers or write it down. As you grow more competent, you lose the need to perform those "somatic components" to solve the same problem. It's also quicker because the somatic components are what took a significant portion of the time. If, however, you're just learning to do without the "somatics", such that it still takes you a comparable amount of time to solve the problem mentally, then it's fairly common for people to pull all sorts of silly faces, humming and erring, sticking their tongue out, stopping anything and everything else their doing to devote the effort to solving that maths problem.
Mental activity is still activity. Yes, you can do it without the song and dance, but it often takes conscious effort to refrain from those visual cues when the activity is significant. Given that most spells take an Action to cast and that an Action could be described as the primary and most significant thing you're doing at any given time, I'm inclined to assume it'll take conscious effort to conceal that Action, even if it's a solely mental activity.