They are great for two types of companies.
The first being 1-man bands, who wish to appear as a small company to internet visitors. This simple format makes it easy for people to understand your products or services almost immediately.
The second business one-page websites are great for are larger companies that offer a range of services, but wish to concentrate on promoting one service in one geographical location. For example you may be a large plumbing contractor, that offers all of the services you would expect from a Plumber. Your main website would promote “central heating installation”, “boiler repairs”, bathroom fitting” and say “solar panel installation”. Your one-page website could be aimed at “Emergency Plumbers in Bristol”. A one-page website dedicated to that service in Bristol.
These websites tend to rank well in search engines, like Google, as they are very content rich on the subject matter.