On x86 systems like Skylake or Zen3, it doesn't even use an execution pipeline. Literally zero resources used, aside from the decoder.
Heck, you can perform "xor rax, rax" as much as you'd like, because that's also a rename. It doesn't use any pipeline at all either.
Register renaming (aka: "malloc" a register) is the fastest operation on modern CPUs. That's xor blah,blah, or mov foo, bar, etc. etc.
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Its only really an issue if you somehow need more width ("Instruction-level parallelism") than what the architectural registers provide.
And even then... I'm not sure if it matters. There's store-to-load forwarding. So any register you write to L1 cache (that is read back in later on) will be store-to-load forwarded, and the whole memory read will be bypassed anyway.
And even then, L1 cache is 4-clock ticks latency, and issued at the full speed of the chip's load/store units. Even if store-to-load forwarding failed for some reason, L1 cache is damn near the speed of a register.