Regardless of trading being based in the pit or upstairs, someone is going to be making markets in those options. The only difference is that they will not be on the floor. What do you think makes AMMs show tighter spreads? It's not lower cost of trading, it's the competition for unsophisticated flow that can be arbed on delta. If a large portion of the market participants are interested in complex orders or if most of the flow is tied, AMMs are not interested (enter an order for something delta-neutral into COB and see how tight the resulting markets are). If there is significant amount of vega risk that's much harder to exploit, AMMs are not interested (look at anything far OTM or longer tenor).
Some products tightened when moved into the AMM world and some products actually widened. In the US, single name options in many specific areas have gone illiquid and de-facto spreads have widened. Bring sx5e options on your Bloomberg terminal and tell me if those spreads look tight (or any major European index) - that market has been fully electronic for a while.
PS. Personally, I'd love for all of the markets to go electronic, since trading voice is a pain. But I don't really expect much of an improvement over the current state.
