For Protocol DAOs
Protocol DAOs who provide liquidity for their native token pairs (e.g. protocol owned liquidity) can open NIL contracts as Buyers to hedge out IL risk on their LP positions. By opening a NIL contract with a Token A strike price equal to the price of Token A when they had initially entered the AMM liquidity pool, they can perfectly hedge out any impermanent loss that would be incurred from their LP position.
This is highly valuable because protocol DAOs can provide their community with trading liquidity, collect trading fees, and potentially earn ecosystem incentives without needing to worry about realizing any impermanent loss of their native token or the base token it's paired with.
Note: ILV claims are paid out in the base token of each token pair. If a protocol DAO purchased IL protection on NIL and the IL on their AMM LP position resulted in a decreased quantity of their native token, they would need to use the ILV claim to swap back into their native token in order to get back to their original native token balance.