> anyone on the path knows the amount of the payment

Thanks to the commonality of multipath payments, nodes along the path only know a lower bound of the amount, not the definite amount

> it is possible to identify recipients, and senders with high accuracy, by only controlling some of the nodes on the path

I do not think this is true. Let's suppose you control 5 nodes along the path (Charlie, Dave, Edna, Filbert, and Genna) and you start to trace a payment that flowed through your nodes. You trace it back to Bob on the "sender" side and Harry on the "recipient" side. But you can't tell whether Bob is *really* the sender or just another routing node. And you can't tell if Harry is *really* the recipient or just another routing node. All you know is, those nodes were as far as you could trace it.

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CA companies likely control 50% of nodes and can get access to 80% of well connected nodes.

Don't you think they would demand government to make LN nodes get a money transmitter license so they can siphon data from those nodes directly if their current setting would not work?

Most LN tx are custodial anyways. You either push for small scale (high failure rate) self-custodial LN that can not be controlled or you set he whole network and its users up for failure.

> Don't you think they would demand government to make LN nodes get a money transmitter license so they can siphon data from those nodes directly if their current setting would not work?

I think they could try, but I don't think it would work. Money transmitters are required to get the KYC info of their users, which is a serious hurdle to onboarding, so I think most users would just gravitate toward wallets where you don't have to do that -- e.g. ones connected to "underground" routing nodes. And thus the KYC'd routing nodes would simply be routed around.