Could you perhaps explain the downside of having multiple market makers per stock? It seems trivial to state that competition in providing liquidity alters the cost of said liquidity and disprove your contention - but why bother to make that argument when there can't really be additional costs by multiple parties competing to offer a service?
With one Market maker the exchange can do so and so it benefits from being a effective place to trade - this is a huge advantage over any other exchange With a second Market maker, the exchnage gain is I believe orders of magnitude lower. Almost any Market maker is forced to maintain sensible spreads (else it is worth trading without them) so just one Market maker will offer expensive but not outrageous spreads. A second one brings only the benefit of slightly cheaper, which coma red to the benefits from the first are negligible
it is unimportant if the Market maker holds for 1 pixo second or one month - what matters is that someone is there to trade. Now HFT is at a disadvantage as they have less scope to make their spread (essentially the other side must already be in the Market) but that's where if all other Market makers disappeared (and the stock slowed down) HFTs must become LFTs and hey presto are indistinguishable from the old style Market maker
yes there is a price point issue but most buyers really have a range they will buy at so more precisely I am conjecturing that there are minimal benefits to an exchange to having more than one Market maker at a given stock within a given price range.
How to provethat - not sure