The explanation is already there in what you quoted — Randall Munroe is simply and quite literally saying that an expression like $(\ln x)^e$ is extremely unlikely to crop up in any situation when working with mathematics either pure or applied.

It's not really a *joke* as such; he's just pointing out something that's absurdly improbable. (I think it's unfair to him to call it a joke and judge it as one.)

Apart from all that, there is also the matter of notation and familiarity. There are certain expressions that recur in mathematics, and outside of calculus textbook exercises it would be quite jarring to find oneself having to find the derivative of $c^x$ with respect to $c$, say, and it's almost psychologically harder to do than to find the derivative of $x^c$ with respect to $x$, even though they are mathematically entirely equivalent.

On notation, Halmos has alluded to this in his *How to Write Mathematics*:

As history progresses, more and more symbols get frozen. The standard examples are $e$, $i$, and $\pi$, and, of course, $0$, $1$, $2$, $3$, …. (Who would dare write “Let $6$ be a group.”?) A few other letters are almost frozen: many readers would feel offended if “$n$” were used for a complex number, “$\varepsilon$” for a positive integer, and “$z$” for a topological space. (A mathematician's nightmare is a sequence $n_\varepsilon$ that tends to zero as $\varepsilon$ becomes infinite.)

Related, from Milne's Tips for Authors (quoting Littlewood's Miscellany, p60):

It is said of Jordan's writings that if he had 4 things on the same footing (as $a,b,c,d$) they would appear as $a$, $M_3'$, $\varepsilon_₂$, $\Pi''_{₁,₂}$."