Small local laws like this tend to gain a lot less traction when they pile up to be a larger (relative) load on smaller, local-only businesses. Rather than not have anything pass, people prefer to pass something which still has 80% of the benefit but only 20% the resistance. Only targeting large chains, at least initially, is a way to move that needle over getting nothing out of principle.

If successful/popular, then it's much easier to pass full coverage later.