Well, first of all, I don't tweet a lot. I don't believe in inane, navel-gazing tweets. Who cares what I had for breakfast, or if I am waiting for a package to be delivered? It is very much appreciated when people re-tweet my blog postings, as those are the main items I tweet about.
I also follow a select number of people and companies. I don't want to make a laundry list to win a prize for the greatest number of people I follow, or for the greatest number of re-tweets. That to me does nothing for my business.
In the business world, you should have something worthwhile to say, or tweet. If you are using social media just among your friends, they may indeed want to know what you had for lunch. In business, not so much.
So should you have a twitter "handle" at all? I think it is useful, because it is important for business owners to be part of the social media world. It is immediate and effective, for good and bad. Your tweets could rapidly go viral and be re-tweeted around the world. Probably more so if your company had done something enormously detrimental and has not reacted appropriately, but it is a marketing tool and needs to be used skillfully. It is not a throwaway component of the internet and should not be treated as such.
Be careful what you tweet and think twice before you hit send. Like emails, once they are out there, deleting your own, original, missive does little if other people pick it up and forward it on. As they say, you can't unring the bell. Make your tweets thoughtful and worthwhile.