The maker-taker fee structure has nothing to do with narrowing the spread, although that effect is consequential. The spread is not caused by any single market maker, but by a collective, i.e. market maker A may quote bid-ask at 100-105 while market maker B may quote bid-ask at 98-101, thus the NBBO (national best bid offer) is 100-101. The spread is narrowed with increasing participation from any attractive fee structure.
Even then, just because the spread is very narrow does not mean the liquidity in the order book is real. For example, a market maker may be co-located near exchange servers to have first priority in receiving incoming orders from others before such orders are posted. And if the incoming orders are going to impair the market maker, it has the incentive (and ability) to change its bid-ask orders. From outside perspective, the liquidity simply disappears. “Experts” would be quick to say that’s just stale orders.
You may have all sorts of theories on the fee structure to the point of reconstructing it into a perfect structure for the most perfect market condition but you may be surprised when market inefficiencies continue to persist. The fee structure does not have 100% direct correlation to the spread.
I wonder why are we discussing about this anyway. Not useful of time and brain power.