I'm not totally sure what you mean by "hedge the inventory risk." How would you accomplish that? You can reduce your position size but that's not hedging, it's just reducing your exposure in the first place. You could use options, but that 1) exposes you to other risks and 2) is prohibitively expensive given the cost to transact in that market is much higher.
The best way to keep risk low as a market maker is to keep inventory low, which means you need to get out of positions quickly, which means you need to have competitive prices to increase your chance of interacting with order flow.
The best way to keep risk low as a market maker is to keep inventory low, which means you need to get out of positions quickly, which means you need to have competitive prices to increase your chance of interacting with order flow.