It is highly relevant when you're being tracked by authorities. They typically start by sending you some money and then watching what happens to it next on the blockchain. E.g. that's what they did in this case where they traced a finnish man's monero: https://cointelegraph.com/news/finnish-authorities-traced-monero-vastaamo-hack

And in the Columbian case (where they ALSO traced a guy's monero) they also relied on the ability of the sender (in this case, Morphtoken) to point out exactly where he sent the money: https://cointelegraph.com/news/chainalysis-leak-monero-traceability

Lightning fixes this.

The simple fact is, on lightning, the sender can't trace his own payment, but on monero, he can, and this difference helps authorities arrest monero users.