How does it break privacy?
Lightning is private for the sender.
Discussion
I have a channel with Kraken so I'm pretty sure if I sent it in one hop from my node it would be easy to figure out. Not that anyone is likely trying right now.
Only the sender knows the total LN fees paid & total hops.
All their node would see is your node providing the final hop to pay the invoice.
You could first route the payment through another channel.
Not in all cases but that's generally correct.