Earlier quoted context omitted.
You can't get rid of mining - that's the cost of trust-less decentralization. You might be able to make mining more efficient, or based around some other finite resource besides computation power (like storage), but even that's a long-shot.
You could make mining more memory bound rather than compute bound, somewhat reducing electricity costs and requiring bigger upfront investments (in DRAM chips). This also vastly reduces the performance gap between commodity and custom mining hardware.
Even altcoins that have tried this approach have seen custom hardware appearing if the coin grows popular enough.
The approach just seems to be a desperate hope that home users will be able to mine profitably, but ultimately it still fails because those with more resources will win out.