Options ARE volatility. The NBBO bid and offer are priced in volatility. The OTC markets don't quote premium; they quote vol-figures. Now imagine trading OTC in which the volatility was essentially fixed.
The OP doesn't understand the mechanics of how volatility trades. It's one thing to have a dealer market (as he proposes) in delta1 as there is no convexity (hence delta@1). Say the OCC were to make algo-markets in single-name options based upon the (30d) historical volatility.
There would be no method by which to price in future micro and macro-events; earnings, dividend-changes; non-farm payrolls, etc. You would have an arbitrarily (cheap) vol-market into earnings in which implied vol could be half of where it should be trading. Imagine how easy it would be to game the system. No entity, public or private, would take the risk of underwriting such a mkt. It would be a massive transfer of capital from the underwriter to the sell-side and HF space (buy-side).
You could counter that by running some sort of handicapping-model in which asymmetric flows would skew the model flat (market vol), but the OCC would go broke before the price normalized. Just one of many reasons why it's a terrible idea. It's the antonym of "free market."
The fact is that I often see complex spreads and combos quoted (on the COB) INSIDE the market in the underlying shares. That alone is proof that the options markets don't need fixing. The share markets DO need fixing (dark pool BS; HFT).
In summary; worst idea ever.