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4. Competing stock markets grow (maybe in another jurisdiction) that allows faster order processing

But faster (continuous-time) order processing results in wider bid/ask spreads; slower (discrete-time) batch processing results in narrower spreads. At least that's what the models show. Follow-up papers even analyze a multi-exchange model (competing continuous-time and discrete-time exchanges), and concluded that investors and retail traders would prefer the discrete-time exchange because it would have narrower spreads (i.e. lower transaction costs).

> At least that's what the models show.

What models? Increasing the amount of risk a market maker must bear will widen the quoted spreads not narrow them since that increased risk needs to be priced in.

The models in the "Frequent batch auctions as a market design response to HFT" paper by Budish et. al.; i linked the slides in another comment.

Since batch auctions use single-price clearing, market makers can post bids and asks without fear of being sniped (so its less risk, not more). And since you can't snipe, they have to compete on price rather than investing in faster connections, resulting in narrower spreads.

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