If you run your own LN node, your channel is associated with your IP, and your transactions are associated with your channel. It is the same as reusing a single bitcoin address for all your transactions, with all the consequences [1], except this time you can tracked down to your physical location. In vanilla bitcoin you can at least generate addresses at will, while opening and closing payment channels every now and then undermines the whole idea of the off-chain transaction layer.

[1] - https://en.bitcoin.it/wiki/Address_reuse