What most small businesses just starting out need is a brochure website, which is basically a virtual business card. The good thing is that almost everyone needs one. The bad thing is that almost everyone can make one themselves–either in WordPress, or Wix, or SquareSpace.
So it’s a funny segment of the market that way. Similar to what @DanCouper pointed out about portfolio websites, it also suffers from the problem that more successful businesses/people will already have people or want more experienced designers. So you will be operating in a market with overall low barriers to entry, but strong competition at the top.
I am not sure I agree in general that WordPress is overkill, though, because even though plenty of clients won’t ever touch it, some expressly want the ability to add blog posts, change pictures, mess with the fonts, etc. A minimalistic WordPress installation is pretty fast-loading and proven. However, the wrong theme or user error can cause some big issues.
In my local market, I know of several WordPress agencies that create simple-ish sites for small businesses–lawyers, construction companies, doctors, etc. If you don’t mind me saying so, the quality bar doesn’t look that high.
However, I noticed that they all offer “SEO” services. To me, that means, to operate in that market, you need to also be able to get/write content, get images, do link development, do social media management, and interface with other marketing. I could be dead wrong, but I think that’s what people mean when they say “SEO”–the days when that meant stuffing your meta tags with keywords and filled footers with hidden reams of nonsense text are long gone.