> Why is this a problem if they lose it when it moves?
Because on monero, the sender knows which of your pubkeys he sent money to and can watch the blockchain to see *whether* it moves
For example, if the pubkey he sent money to never appears in a future ring sig, the sender knows the recipient still has that money -- he knows it hasn't moved
That's bad for receiver privacy. What if you don't want him to know? Why *should* he know? What if, at some point in the future, you claim you sold all your monero, but an exchange proves that they sent money to your pubkey, and the monero blockchain proves it hasn't moved since then? That's a serious privacy defect.
And that's not the only defect. You say "they will lose it when it moves" but some blockchain analysts have managed to track what happens to monero after it's sent by eliminating some or all of the decoys used in monero's ring signature scheme. Chainalysis even offers a paid service where they brag about their ability to do this, and law enforcers have used this service to arrest monero users. So your claim "they will lose it when it moves" might *sometimes* be true but monero provides no guarantees here.
That's why *omitted* information is better for your privacy than *obscured* information. Monero *obscures* details about the transaction. Lightning *omits* those details altogether by (1) not posting anything to a blockchain (2) actually encrypting all parts of the transaction (3) using HTLCs and (sometimes) rendezvous routing to ensure that the sender can't even be sure he knows the recipient's public key