When you open business bank account, for example, Chase business checking account, they ask you to fill in your “primary business address” which they could very well check with what you have in the Secretary of State records. Same can do my city business unit, not sure it’s good idea having totally different addresses in those systems, they all call it “primary business address”, so I bet they mean the same thing, so specifying your home address while having different address on file in Secretary of State is kind of lying
I can’t say for other cities, but in Pleasant Hill Ca, rules are: 1) every business ought to get a business license, regardless of its type, including mobile 2) the business should have physical address with space where you can work, either real office or your home