Yes. We don’t even need to prove it, it’s common sense:
If a spammer can programmatically submit any number of requests before PoW, and then after PoW they have to spend even just 5% more compute...
Exactly. Incur costs on the spammer without annoying legitimate users. It's a scaling issue. Running proof of work on a single note is inconsequential. Running proof of work on millions of spam notes starts to become more costly.
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