I am still searching for the flaws in another idea I have for an improvement to Proof-of-Work. I had mentioned this is in a prior discussion with monsterer in my thread.

The idea is every transaction must include a PoW share.

There are many details to getting this correct and I believe it ties in with enabling instant transactions as well. But I need to write this all down and make sure there isn't a flaw.

My helicopter perspective thoughts are that it can force the difficulty high enough that mining becomes unprofitable (assuming debasement is a small fixed percentage say 1%). This will drive away the professional miners and thus stop the dumping of coins which drives the price down. It will also limit the electricity cost per transaction to some minuscule amount and not Bitcoin's $16 per transaction electricity cost. I see now my 2013 thread Spiraling Transaction Fees concept is finally getting serious attention.

Thus hopefully it can make it much more difficult for the government to regulate mining.

This is probably my last attempt at a solution. Seems I was thinking about this in the past and I thought it was flawed because servers have to aggregate data for transaction signers and I thought these could be targeted by the government or otherwise centralized. But what remains true is that if the transaction signers have more PoW hashrate than any miners the government can regulate/control, then the permissionless principle seems to hold.

Since mining becomes unprofitable then selfish mining attacks don't matter.

I think this is the most promising direction that still remains for me. Everything else looks like a waste of time.