So for example in the x * 2 case, if you canonicalize it to a shift, the representation of that shift may have other properties (or tags or whatever) like “this operation has no side effects on memory”. A later pass might make sure the register is saved (or decide to discard the shift because its result is not used) without* that pass having to know specifically about shifts.

Later passes could have different canonicalizations, say coupling the shift and its store so that a single thing is, say, hoisted out of a loop (this is actually probably an unrealistic example, but reasonable for explanatory reasons)