Unfortunately, you are assuming the most fantastic scenario. 
What can I say, I'm an optimist Quote
Let's consider the most efficient option: one LN node and many end users connected to this node. The node must invest the same amount as all users do. If the node wants to earn 3% of the profit for the year, then all users will have to pay this 3%. That is, on average, each user will pay 3% per year of the amount invested in the channel. (The average route length will be 2).
3% sounds bad if you spend $1000 per month. But if you put $100 in a channel, and spend and receive $10 at a time, but do that 50 times per month, then $3 in fees doesn't sound bad at all! I spent more on my last on-chain Bitcoin transaction (I made a mistake on the fees, my fault).Quote
"Super-cheap transactions in LN" and "LN-nodes that make a profit" are mutually exclusive things.
You're probably right here. But I don't really mind, it's not as if Bitcoin nodes are currently making a profit. Some things are just done to support the network, and if an exchange (or casino) runs a LN-node, earning money from transaction routing is only a side-income, and not their core business.Quote
In 2017, there was an article dedicated to this issue.
https://medium.com/@jonaldfyookball/mathematical-proof-that-the-lightning-network-cannot-be-a-decentralized-bitcoin-scaling-solution-1b8147650800
I must admit I don't have the time to read it in-depth now. But I like this picture:https://medium.com/@jonaldfyookball/mathematical-proof-that-the-lightning-network-cannot-be-a-decentralized-bitcoin-scaling-solution-1b8147650800
(source)
The thing is: I'm okay with the scenario on the left, if that means I can make many small cheap payments using Bitcoin. I'd prefer a fully decentralized system, but I get that won't happen.