I'm just taking it as proof that my right hemisphere isn't entirely dormant... (or would this still be more of a left brain activity?)
It is certainly possible to do very effective kerning using a purely logical/rote approach with no intuition. (Proof: a computer can be programmed to do it.) However, this requires paying close attention to detailed aspects of the letterforms that most people never notice. It also helps to use a ruler and a calculator. Nonetheless, this is probably the fastest way to get the kerning obsessively close to perfection.
I suspect what almost all typographers actually do, however, is "just eyeball it". This is MUCH faster, and the results are typically close enough that only obsessive or neurotic people (or software designed for the purpose) will ever notice any inconsistencies.
A third option is to just pigeonhole all your characters into a dozen or so "classes" (round, flat, sticks out on bottom, sticks out on top (capital), sticks out on top (lowercase), ...) and kern pairs of classes. This is very quick and easy, and the results are much better than if you don't do any kerning at all. It does tend to leave you with a handful of less-than-ideal pairs, though (e.g., qj may look bad, although that will seldom be noticed in the English-speaking world; if there's a particularly bad combination that's common, you can fix it with a ligature and not have to break up your classes).
Excruciatingly bad kerning, like in today's comic, happens when somebody not only fails to bother to do any kerning at all but furthermore isn't even consistent about the left and right space on each glyph. That capital C just plain has unnecessarily much space to the right of it. It would probably be more space than you'd need even if the next character were a capital X, and it's certainly far too much for the average case.
The real nightmare, of course, would be if you had to do kerning for a living -- working for a font foundry where somebody else does the creative work of designing the letter forms and you just kern them. Bonus points if you're assigned a set of full Unicode fonts (including all the Chinese characters and ancient writing systems and languages with 1347 native speakers and everything) in a full range of weights, with both sans/gothic and serif/mincho versions. A person could spend a lifetime obsessing over the details, gradually becoming more and more insane, more and more incapable of thinking about anything else than kerning, until the mere idea that they might change the shapes of some of the characters in the next version of the font set keeps you up nights.