Why Is the Constant Sum Formula Unsuitable for Volatile, Non-Pegged Cryptocurrency Pairs?

The Constant Sum formula ($x + y = k$) is unsuitable because it offers infinite liquidity at the current price, leading to zero slippage. For volatile, non-pegged assets, this would allow arbitrageurs to completely drain one side of the pool with a single trade whenever the external price diverges slightly.

This design does not protect the liquidity pool from large price movements, unlike the Constant Product formula which increases slippage as the ratio diverges.