I believe punishment is an inaccurate term. Two cultures, one earnestly striving to be a pure meritocracy and the other firmly entrenched in the recognition of birth privilege and honour, are here intertwined with each other. Assignment to Kamchatka, and other eastern posts, becomes the solution for how to reward behaviour seen as beneficial by the meritocracy but offensive by (some member(s) of) the aristocracy.
I suspect that the "offensive" behaviour being ostensibly punished might frequently have been strict obedience to orders against aristocratic pressure. When said offended party demands satisfaction from an officer for such behaviour, the meritocracy needs to both visibly appease on the one hand, and visibly reward on the other. Five years out of sight and out of mind, at a higher pay and responsibility, fits nicely to my mind.
On a deeper level, an assignment that would be seen as punishment by an aristocracy obsessed with its constant personal contact with peers at court in Moscow and St. Petersburg might well not be viewed as such by an organization dedicated to rewarding competence. A lower standard of living in the East might have provided an ambitious officer with better chances of saving a small nest egg. Less frequent inspection by, and even correspondence with, one's superior grants a first taste of independent command. If all (merit-based) appointments above a certain rank require completion of a hardship posting, well why not just get it over with?