Well presented! In reality, MM do delta hedge but less on gamma

Hedging costs money but reduces the variance of your return. Most MM delta hedge daily using individual underlyings, some use index future (to save trading cost. of course it comes with a larger variance). It is theoretically impossible to do gamma neutral hedge. It is just going to taking off most of your profits. Normally they control individual net gamma position under a limitation, and over a large book, they matain a relative neutral (close to 1) Long/Short gamma ratio across different underlyings.