PoW is unbalanced and ultimately an unworkable solution due to attackers having more resources than ordinary battery limited mobile users.

People will waste time implementing this. It will seem to work for a while. Then a malicious attacker will bypass it with ease at no cost to themselves.

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PoW doesn’t need to be done in your phone.

You can pay someone else to do that, or have your own PoW rig at home do it for your phone.

I’m not talking about doing a billion hashes on a phone battery.

If that’s the proposal I agree it makes no sense.

That doesn’t mean abandoning PoW

OK you're right. If you're talking about renting time from the fastest ASIC that's actually an unfakeable cost. That would be a meaningful rate limiter!