> The service would give the request a priority value based on the "difficulty" of the puzzle solution.
Seems like single clients could increase the difficulty to higher than what the bot net would do (so it gets priority), and hence get access. Operators of the bot net would probably hard code one value as the difficulty, and it would be lower than what you could typically set on consumer hardware.
Maybe user agents could even do this increase automatically?
Bad assumption.
Assumptions like these never last. People who say “I don’t have any money” are still valuable to hackers as phishing senders, legitimate social media accounts, residential + non-cloud + regionally convenient IP space, etc. If consuming connection / server resources becomes valuable then botnet controllers will find a way to pay the cost. It’s easy because someone else is paying for the hardware, bandwidth, and power costs.
But the effect of a market of PoW is the same — there is game theory involved in bidding (just like a silent auction). Even if a botnet uses a dynamic priority bid system, the cost increases as the botnet tries to starve the server of resources. The server’s resources are always zero-sum and the bidding will get progressively more expensive until the opportunity cost of the botnet changes behavior.