They aren't doing it because they want the law to be enshrined; they are doing it to have the law challenged.
They have the full resources of the state. They can drag the case out in the courts for years. Meanwhile, the Left is spread thin, because every dollar spent fighting this law is a dollar not being spent putting up better candidates.
GOP gets to use taxpayer money to fund their little projects, while Progressives have to pay to fight for freedom.