Here's the most compelling reason why you should offer newsletter subscription:
People might not decide to sign up to your RSS feed or email alerts for your blog. They might however be interested in a newsletter, predominantly because it is only sent once a month (unlike a blog email alert, which is usually sent daily.)
So offering a newsletter is a great way of capturing that demographic.
By sending out a newsletter once every month, you can assure that your brand stays front of mind. By staying front of mind, you have a greater chance to collect a purchase from the client once they need your service, product or recommendation for affiliate products.
What to put in a newsletter? Find out the problems, needs and desires of your demographic. Write solutions for their problems, or posts that fulfill their desire for a particular type of information. E.g. an accountant can send out a monthly newsletter with tips and tricks, latest legislative updates in plain English and interesting articles such as "what really happens if you don't put in your tax return on time".
These articles give the accountant a chance to show off his expertise, thereby winning the trust of his audience who one day, when they are in dire need, might call upon his services. Or if they are already a client, they might forward the email to a friend (word of mouth!) or be able to conduct an intelligent conversation at a party because they read one of the articles. When their friend than asks "how do you know all this", the client can tell them he read it in the newsletter sent by his accountant (word of mouth again!).