I would call silent payments a steganographic method of hiding information because it allows you to get lost in the crowd merely by making completely normal payments with no specific fingerprint. With silent payments you are hiding in plain sight.
I realized another drawback: the receiver needs their private key to even know they've received a payment. That makes a watch-only wallet impossible, and even if you use Bitcoin Core, private keys are stored encrypted until you enter your password. Keeping the wallet unlocked adds a security risk.