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Maybe, the proof of work can run in the background.

Or it can run as part of a checkout wizard's "verifying your browser and processing your payment, don't close your tab" step.

At which point it exists solely to punish real human users? What scraper bot is going through checkout?

The credit card tester bots go through the checkout process.

PoW wouldn't be a big issue for them though since their volume is much lower.