Your first point: creating fresh, relevant content on a regular basis, is the key one. This then hooks into catching long tail searches relevant to your business. The more you talk around the subject and business, providing use-cases, how-to guides, 37 things you never realised about x, the more long tail searches you're likely to catch. It's also far easier to place on the site as a blog post than trying to constantly produce evergreen content for the site and find some suitable place to put it.
It's also the logical place to inject a little opinion or humour - which perhaps will lead to some discussion or following. For the most part that's going to look out of place on the main site in amongst the sales pages.
For many small businesses, in many sectors, building a significant following is unlikely, unless the posts are very far removed from the business: perhaps drain clearing, dentistry or invoice factoring. In such a case you're never, ever going to build the same following as if you were in some entertainment or tech sector discussing the the latest iThing. I'm sure there's one or two exceptional folks out there who've managed to gain following for some dry, dull industry, but that's infinitely more about them, than the topic.
Many of the businesses that blog, highly successfully, are blogging about topics incidental to the business - for many web businesses the topics that catch notice and generate responses are the discussions about programming or some problem they encountered with scaling or the tech they're using, rather than the payment service, or the service they're actually offering. The posts on the actual service they provide getting much less traction and sharing by comparison.
But it's also about getting awareness, so that post on some uncooperative aspect of Wordpress or Apache might introduce new people to your actual service. Of course this perhaps easier in tech, but in any sector there are connected and related sectors where the same can apply, so the wider the topics the better even if not directly related to the business. That's not the same as saying constantly blog about iThings on your dentistry site of course!
Establishing self as authority. Again for many sectors, this is a bit of a stretch. With the best will in the world, the most surprising, enlightening posts on drain clearing are unlikely to get much traction on Google+ and Facebook, yet the engines are taking social success as a clear sign of authority. I've seen several valiant attempts to make "unsexy" businesses succeed on social, and to an extent, they have. As an example a ladder and scaffold rental business spent much effort sharing photos of ladders in silly places, and achieved some success. Up against shares of an iThing, cats and zombies, not so much.
So, yes, it's very necessary, particularly for the very noticeable effect of long tail traffic. For the other factors, treat them as nice-to-haves and blog accordingly.
The other key thing about blogging is nearly everyone gives up far, far too early, so keep at it.