At the risk fo stating the obvious, this is not automatically true. Specializing makes for easier marketing, but not necessarily higher rates. Some clients just don't have a lot of money to spend.
Specializing allows you to target the ones who do. Cast a wide net across "local businesses" and you're going to get a lot of boots and toilet seats to keep your tuna company.
At the risk fo stating the obvious, this is not automatically true. Specializing makes for easier marketing, but not necessarily higher rates. Some clients just don't have a lot of money to spend.