What Is the Primary Drawback of Using a Constant Sum Market Maker for Volatile Assets?

The primary drawback is that a Constant Sum Market Maker (x+y=k) would be completely drained of one asset by arbitrageurs almost immediately. Since volatile assets' prices diverge, the pool's internal 1:1 price would quickly become misaligned with the external market.

Arbitrageurs would buy the underpriced asset at the fixed 1:1 rate until its reserve reached zero, leaving the LP with only the overvalued asset. This results in a total loss of the initial deposit's value in the drained asset.