FICO to incorporate buy-now-pay-later loans into credit scores

They didn't before? It's a credit like any other type, increasing debt burden like any credit. Seems like corru... ahem, lobbying of course. :)

Your credit score can decrease if you pay off your credit card balance or pay it down too quickly. For example, paying off the last $10k on a home loan. The score is also a reflection of your value to them as a paying customer. How much money you can make them, and how reliable you are with regular payments based on past data. These types of businesses may seem off, but if the customer is reliable and makes you money, assigning a low score based simply on the business type is a recipe for litigation.

That is true when you close an account (like paying off the last $10k on a home loan), but I don't think that is correct when paying a credit card down to a $0 balance and leaving it open.

The reason is that your credit score is impacted by both your available credit (higher is better) and credit utilization (lower is better). When you pay of the last of a home loan and close that account, your available credit goes down and your credit utilization goes up (assuming you had any other debt). Both of those hurt you. When you pay the credit card down to $0 and leave it open, your available crediot stays the same and your utilization goes down.