Why Are “Stableswaps” or Similar Curves Used for Stablecoin Pools Instead of $x Y = K$?

Stableswap curves, like those used by Curve Finance, are designed to offer extremely low slippage for trades near the 1:1 peg, maximizing capital efficiency. They achieve this by behaving like a constant sum formula ($x + y = k$) near the peg but transition to a constant product formula when the ratio diverges significantly.

This hybrid approach supports large trades without major price impact while still providing liquidity during a de-peg.