I’m thinking that “Excess” as used in the OP is referring to “Excess of the voluntary market”. We have a personal lines company that is part of the Excess & Surplus variety that is willing to write coastal homeowners risk that our main company won’t write.
Excess Lines in this context is the ability for the company to set rates/premiums w/o regulatory approval (might still be subject to regulatory review, though) and are usually for those risks that the voluntary market may not be willing to write (e.g., the coastal risks) or will charge a very high rate due to lack of expertise in underwriting the risks (the rate being a deterrent for the customer). I can see some smaller commercial risks that have enough “odd” exposures that would benefit from an Excess Line cover.
And the Excess in this case may not be just for liability coverage, but also property that the voluntary market will explicitly exclude.