Let's be clear--you can absolutely build an incredible company without participating in social media. There is certainly success without blogging, and blogging definitely isn't a guarantee of success by any means.
So why bother?
You have tons of things to do as a founder. You have hiring to do, money to raise and you've got to get your company's story out there. Blogging takes up time that you don't have.
Most entrepreneurs don't recognize the value of personal use of social media as an important--maybe the most important--channel for accomplishing these milestones.
Two things are true for every startup: 1) Founders and CEOs are key to driving success and 2) these companies need awareness for their unique message to accomplish all sorts of goals. Yes, the entire team does the work, for sure, but founders and CEOs set the tone with their first hires. The initial team and the level of work they are challenged and motivated to do is a direct result if the environment created by the people at the top. That's why startups are uniquely personal. The DNA of the founders makes its way into the product, sales strategy, recruiting efforts, etc. If you are going to accompany these efforts with a public message, you're going to want to choose an equally personal channel.
Unfortunately, using other people's channels and audience, which is essentially what PR is, won't be as effective--simply because no one can tell your story as well as you can. PR can magnify, distribute, etc., but it's your own story that is the fuel for a well executed PR campaign these days--and I think it starts best on your own site in your own voice. Your blogging or participation on Twitter won't suffice alone, but it's a key ingredient to a comprehensive PR strategy these days.
On top of that, no one really gets paid to tell *your* story--but that's what people want to hear. When people consider working for you, they want to hear who you are and where you're taking this company. You can tell them on the interview, but how many people aren't even coming for an interview because they haven't heard about you and your story?
That's part of what blogs, Twitter and other forms of social media do--they make you discoverable. They also make you more easily followable. I can watch your napkin develop into a company from afar without further cluttering my inbox--not that email lists are easily discoverable anyway.
These channels also allow you more at-bats with your message. You don't want to spend your whole NY Times interview telling the whole story about how your grandfather's shoe store inspired you to be an entrepreneur, but you can tell that story on your blog--as well as any other lessons he taught you. That story might surface a VP of Marketing with an interest in startups who has a similar story of family inspiration. That person may have been following you based off of someone else's retweet of that post you wrote on why good marketing talent is so hard to find. A coffee and a handshake later and you just added a key member of your team who was enthusiastic enough to take a huge pay cut in exchange for more equity, without paying a recruiter fee. What was that you were saying about what your time its worth?
Blogs and social media can be as equally serendipitous in surfacing early customers, speaking opportunities or potential investors. Yes, it is absolutely entirely possible to do this on your own, but why not use a cheap channel that works effectively if it is available to you.
Time, that's why--but there are ways to solve for that. If I was a busy entrepreneur with a commute, for example, I might record my thoughts over audio and get a ghost writer to summerize them into a set of discrete posts. In fact, getting interviewed for an hour by someone could result in enough content for 3 or 4 blog posts--since you can speak faster than you can type. Is this inauthentic? Not if you're conveying your unique perspective, experience and message--it's no different than having an editor. How about having everyone in your company contribute suggestions for things they'd like to hear you talk about--take requests if you can't think of what to write about. Anything, really, that is you being the face of your vision and your company, telling your story is a potentially valuable asset--one that I don't see nearly enough entrepreneurs taking advantage of. Instead, they spend way too much time trying to convince others to tell their story for them.