Right. If you were to use something like Kraken (which requires identity verification / KYC) to pay the lightning invoice using your account balance at Kraken, you probably don't want them to have access to data that would indicate this was a P2P trade on RoboSats.

The problem was that order information on RoboSats is public. So, for example, let's say one of the 87,000 new IRS agents asks Kraken to share the invoice info from withdrawals made, and they see that Bob made a 3M sat withdrawal (~$750) for order #12345, they can then find that order #12345 was where the seller (Bob) sold bitcoin at $25,000. And Kraken shows Bob previously bought that bitcoin at $18K. And Bob didn't report any capital gains for that year. That becomes a problem. By simply not including that Order # in the LN invoice description, the ability to link the LN withdrawal from Kraken to a specific order on RoboSats is essentially impossible as only the buyer and seller have that payment reference GUID information that Kraken would have seen.

That's one example. Another is where, let's say, a data breach at Kraken reveals that Alice (buyer) has received dozens of LN deposits into her Kraken account, and from those RoboSats order numbers from the LN invoices it can be seen that she uses Zelle as her payment method used when buying those sats. And then Zelle terminates her account as a result. Nobody wants or needs that.

Good question. Maybe because the Order number is how the trade is identified. For example, the path in the URL for the order is /order/nnnnn

If you have multiple offers, having the Order number makes it easier to verify that you are paying the right invoice, or makes tracking a payment later easier.

Or maybe there is another reason that I'm not aware of.