You can think of one or many Cashu payments as a deferred Lightning payment. Especially useful for asynchronous transactions: A merchant can always accept ecash from any mint and, depending on their appetite, either swap out to mints they trust or to a non-custodial Lightning wallet when they come back online and need to process orders.

As a merchant, you can't get rugged if you never received the actual payment.

On the other hand, sellers can also define the mints they require a token to be from (Cashu payment requests contain this information). That way, the sender is expected to get ecash from a specific mint (typically using Lightning). These transactions are typically instant.