You would not want to do this if for some reason you wanted to anonymize the sender or at least act as a proxy to protect the sender's information (as you noted

You would not want to do this if for some reason you wanted to anonymize the sender or at least act as a proxy to protect the sender's information (as you noted). But another reason is publicity/visibility - startups need plenty of name recognition, and having your name be associated with a useful service is certainly one way of doing it (as long as your customers don't end up classifying as "spam" like the OP's customers).