The wiki entry for Conjunction Elimination, sometimes called simplification elsewhere $$ {\frac {P\land Q}{\therefore P}} $$ is classified as an inference rule, rather than replacement rule.
This transformation feels closer to a replacement rule like double negation elimination, rather than an inference like Modus Ponens, because it operates on only one proposition, and doesn't seem to produce anything novel (at least as much as inference rules typically seem to do)
What are the technical reasons for this classification, and are there any thought experiments to see it as more intuitive?
After pondering the arguments for and against each choice, I'm left wondering if there is even a meaningful distinction between inference rules and replacement rules.
The fundamental difference between rules of replacement and rules of inference is that the former are based on logical equivalences, while the latter are based on logical consequences.
This distinction results in two major differences in how you apply them:
First, replacement rules can go ‘both ways’, e.g. a replacement rule based on the double negation equivalence $\phi \Leftrightarrow \neg \neg \phi$ allows me to infer $\neg \neg P$ from $P$, but it also allows me to go infer $P$ from $\neg \neg P$. On the other hand, inference rules go only ‘one way’, e.g. using Simplification you can infer $P$ from $P \land Q$, but trying to infer $P \land Q$ from $P$ does not follow the pattern of Simplification. And that is for good reason, since the former is not a logical consequence of the latter.
Second, replacement rules can be applied to component statements of larger statements. For example, using double negation you can infer $P \to Q$ from $P \to \neg \neg Q$. On the other hand, inference rules are only applicable the statement as a whole. So, for example, you are not allowed to infer $P \to R$ from $(P \land Q)\to R$. And again, that’s a good thing, since the former is not a logical consequence of the latter.
Finally (and maybe this can be regarded as a third practical implication of the fundamental theoretical difference), rules of equivalence always infer a statement from exactly one other statement, but rules of inference can involve any number of statements. As you point out, Modus Ponens takes in two statements, Constructive Dilemma (from $P \lor Q$, $P \to R$, and $Q \to S$, you can infer $R\lor S$) takes three, and Law of Excluded Middle (from ‘nothing’ infer $P \lor \neg P$) takes zero. So, if you have a rule of inference like Simplification, which takes one, it may very superficially feel like a rule of replacement, but as already explained it really isn’t.
The only commonality between rules of replacement and rules of inference is that both can used to infer a statement from some other statement(s). As such, both kinds of rules can be said to be inference rules, but as explained above, rules of replacement are fundamentally distinct from rules of inference.