A website should run its self once set up.There is a masssive difference between being a self employed plumber (be it under guise of ltd. ) and a plumbing business. Just being a plumber is extremely demanding. You simply can't expect a man to be sweating joints in the morning and then analysing his website traffic in the afternoon. This is why anything that I would call a conventional business would have a technical or front of shop level worker, and another person whose sole concern is the website clicks, twitter posts, branding, recruitment etc.
Trying to do both things at the time might work for a bit but long term one or the other will always get neglected and we arrive to the point of state of things about which your post is based.
But i hear you.