I own a manufacturing company. Started out working out of my house quoting widgets and subbing out all manufacturing work. Then I bought out a vendor, so now I have all the joy of employees, a facility, property taxes, etc.
My engineering background is what helped me figure out better ways to make widgets, and design new ones as needed. Now, however, I try to look at my company itself as the "product", and work on ways to improve its functionality, robustness, and efficiency. Looking at it that way, good engineering and good business are not dissimilar. As ajack says, you can pick up the detailed non-engineering knowledge needed as you go along. If you made it through differential equations and higher engineering math, basic accounting shouldn't be too hard.
You may be right in that most non-consultant company owners have left most of their engineering, and these types of boards, behind. It's a rare and nice day for me when I can spend 4 hours or so on design work. As a manufacturer, I don't get paid for my time spent on a clever design, but if I designed it well enough I can potentially get paid over and over again as I manufacture it, which is nice. Of course, I have to figure out whether there is a market for my widget, and I have to be cleverer and more cost efficient than my competion, without being so clever that he takes my design and has it manufactured at his factory in China and starts undercutting my pricing.
On the flip side, are there any engineers out there that own consulting companies, but no longer do any actual engineering? Or do all consulting firms become partnerships as they grow, sharing the executive burdens among several partners while allowing them to spend a significant portion of their time doing billable engineering? I could see pros and cons either way, depending on what you want.