Question: does the Lightning protocol allow you to overpay fees? I'd assume so: checking that the fee is identical to the required fee isn't necessary.

Why am I asking? Because the combination of round payment amounts and public routing can be used to deanonymize payments. Eg if Alice sees a payment of 1005 sats, and Alice knows that the only route that would require a fee of 5 sats on 1000 is to Charlie via Bob, Alice can make a pretty good guess that the payment is intended for Charlie.

Since LN fees are so cheap, it'd be perfectly reasonable for wallets to intentionally overpay fees a bit to increase the anonymity set of where payments might be going.

Related: I recently changed my default tipping settings to be not-quite-round numbers.