> I think lightning needs economy of scales in order to minimize the bitcoins "locked" perception, because once you can pay lots of your needs with lightning then those bitcoins are not "locked" anymore.

What do you base this assumption on? Once there’s a gateway between a consumer and a merchant, then sending e.g. 0.001 BTC from the consumer to the merchant happens by the consumer sending it to the gateway in one payment channel, and the gateway sending the same amount to the merchant in a separate payment channel. It’s atomic, so the funds are guaranteed to arrive, but it requires locking the amount that the merchant expects to receive in a payment channel between it and the gateway. This is how the LN protocol works.

+1, AFAICT what you said is accurate (^.^)

But LN is more productive in an interconnected economy

Let me take your own example to the extreme case and let's assume every entity in the world has a channel opened to only one gateway.

    e  e  e
     \ | /
    gateway
     / | \
    e  e  e

With this topology, only this gateway has its bitcoin "locked" but earn fees routing, everybody else is free to move their bitcoin to whoever they want, as long as the gateway has enough bitcoins "locked" with the receiver. But keep in mind that the gateway can move x100 the volume of bitcoins they have locked, because money moves back and forth

I think a more decentralized topology, where most entities are gateways too, will have less bitcoins "locked", but I don't know by how much, 30% less?, 70%?, 95%?, I'm not sure, but I think it's probably better than last scenario.

Nevertheless, no matter how good the LN gets, its inevitable that some bitcoins will indeed get locked, when any gateway spends all of its bitcoins then everybody else connected to that gateway cannot route payments through it, and unless they intend to pay directly to the "bankrupted" gateway, those bitcoins are indeed locked.

I think no matter the scenario, LN reduces the need to transact onchain, and the better interconnected the economy is with the LN, more effective it is at doing so. So I think a better metric to follow is the #-of-onchain-bytes that were saved thanks to the LN

Another thing to point out is that we are talking about the LN that is deployed today, we haven't taken into account future improvements that might come, like multiparty channels.

I think the serious technical problems that the LN really has today, is that it's not that robust for gateways, I've heard it has DoS weaknesses, and privacy issues, and I'm not sure how solvable some of them are if the topology becomes centralized with just a few gateways