It's pretty simple: a unidirectional LN channel that does N transactions in its lifetime decreases the total transactions that need to be done in the bitcoin chain by a factor of approximately N.
It's very easy for this tradeoff to be worthwhile! Eg consider the case of a mining pool that opens a new channel to a big routing node with the block reward. Those channels will inherently be bidirectional. But with just a few transactions, they can pay thousands of individual hashers. The big routing node will of course have to do transactions themselves to make use of the funds on their side. But they're in a position to amortize that at scale too, eg with transactions opening channels to big exchanges.
The only thing the routing node has to do is be careful to ensure that their overall fees are sufficient to pay for the necessary transactions. We don't have this yet in the LN protocol, but fees on incoming payments will eventually make this quite easy to achieve in an automated way.
If we assume that there will also be N hops, and each of the N hops to support the N transactions, then doesn't everything cancel out in the end? Sure, a single hop that handles 10 transactions will replace the 1 on-chain transaction, but that's 1 hop. The other 9 hops also do the same thing, so in the end, 10 transactions require 10 on-chain channels (one channel per hop).
In the mining case, let's say there are 10000 participants in the pool. Then it needs to open 10000 channels. Now if the pool has a ton of BTC up front, maybe it can benefit, but it's pretty painful to create these giant channels for each participant up front. And a participant might disappear, in which case, you pay the closing fee and then maybe open a channel for a different participant. This "churn" of channels can become rapidly expensive.
Now if you say the mining pool doesn't need to open a channel to each participant, now the participants are stuck without inbound liquidity. They can buy it, but that's again, on-chain TXs for each one. And that step to buy liquidity is not exactly easy or cheap.
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