It's not true that traditional code generation approaches ignore this problem. Copy coalescing is a well-studied problem - the problem is that solving it optimally is expensive enough that compilers use heuristics[1]. Sometimes they don't do what you want. (Any reasonable allocator should catch the case that you mention, though.)

Higher quality compilers will also try things like commuting instructions, using lea as a three-address add, etc to avoid a move.

[1] Some recent progress on register allocation over SSA may improve this situation, but I don't think that work has made it into production compilers yet.