The liquid staking journey ends the moment you supply liquidity.
Liquidity pools are the lifeblood of all of DeFi, and without them - LSTs would be unable to see any meaningful downstream adoption, nor independent demand. The issue with them currently however, is that the "liquid" aspect of liquid staking ends abruptly after a user deposits them within a liquidity pool, as the resulting LP tokens are very one dimensional with few usecases - somewhat defeating their purpose with no real alternative due to how fundamental LPs are.
LP tokens rarely have any utility outside of staking for additional rewards, and aren't easily composable for DeFi although there are a few novel approaches to supporting them within applications (crosschain applications are of course borderline impossible). Adoption however is extremely slow due to the sheer number of dexes and liquidity pools that exist, and Uniswap/Curve pools prioritised due to their TVL which may not offer the greatest APR. This dilemma is compounded by the fact that LST pools are towards the bottom of the list when it comes to urgency, as TVL would be prioritised for obvious reasons.
As it stands, LST holders either provide liquidity on dex's for sub-par APR subsidized with token emissions, or use them directly within downstream DeFi applications.
There is also the issue with how LP token values are determined - since they are merely a receipt of your share of tokens within a liquidity pool. As a result, they're very volatile in terms of value as they are affected by the price movements of (at least) 2 assets, as well as the composition of the underlying pool.
Combined with the fact that there is little to no demand to trade or swap LP tokens (due to lack of utility and would also require liquidity pools that contain LP tokens which are somewhat illogical although it has been done successfully), acquiring a price feed for them is next to impossible from an oracle's perspective. Instead, protocols like Aave have to rely on an "estimation" of the LP token's price, based on the value of the underlying assets (which would have their own independent price feeds) as well as the composition of the pool and is calculated by a dedicated smart contract - which of course introduces it's own additional risk and inefficiency.