L2 protocols are not ever going to have anything similar to PoW-type mining because they rely on the L1 layer.
But, contributing power to a pool doesn't pay you on-chain without trusting the pool. I haven't tried this ever, but don't you get pool shares firstly and then you give those for BTC? Wouldn't it be better if you were rewarded every hour, off-chain?
When you mine via a pool today, the pool will periodically payout your earnings. If someone was earning enough, they could receive their earnings every hour.
I also don't think it would be feasible for pools to offer LN payouts if the pool is obtaining its revenue from block rewards (as opposed to selling hashrate to a third party). The pool would need to consistently by opening new channels, and the miners would likely be consistently closing channels.
I am not sure what the payment structure is for most pools today, however there are many payment structures that depend on the pool's performance over periods longer than one hour.
Also, let's not forget that: LN is essentially PoS!
From an earnings perspective somewhat, but not from a governance perspective.
If you have a single LN channel open with a large capacity amount, you are not going to earn any revenue, because there would be no routes going through your node. Going a step further, if you have a small number of channels open with a lot of capacity, your node may not get much traffic, depending on the network topology. If you have many channels open, with a fairly small amount of capacity, you may earn more than the person with larger capacity if your open channels are well placed within the network, such that many people route payments through your node.
PoS nodes also can choose which transactions to confirm. With LN, it is not possible to choose which transactions to allow (other than by amount of the tx and the amount the participants are paying your node).