Maybe the PoW function should be made as simple as possible, so that ASICs can be devised for it very easily.
The design of such ASIC could be open sourced - removing the barrier of entry, ensuring a level playing field.
Then, every device on the planet can easily be fitted with these ASICs and the overhead of doing would be negligible for HW manufacturer.
I do not think it would be necessary to reward miner in a heavily decentralized scenario (say, > 100M miners) - the fact that you would get secure transactions for the cost of the energy you spend seems to be enough of incentive.
Then, I also believe that any user node should (must) be a mining node.
That is, it should not be possible to use the system without contributing to mining.