A small claims court would usually be a poor choice of court to get the results you seek, although they are not entirely without jurisdiction over these cases.
Most small claims courts in the U.S. (and by the way, there are no federal court small claims courts) do not have the authority to issue injunctions or declaratory relief. Typically, they can only award money damages and can only do so up to a modest jurisdictional limit (typically $1,000 to $10,000 depending upon the court system). This is a big problem where money damages for breach of an open source license are difficult or impossible to prove.
For example, a small claims court would not have jurisdiction to issue an order requiring that: "the source code in question be made publicly available."
Also, usually a U.S. small claims court allows only in person hearings (often only one for the whole case) and does not have pre-trial disclosures and discovery, or motion practice. Often they do not allow parties to file written trial briefs prior to the hearing. So, getting the necessary facts lined up, avoiding surprise, and educating the court about the law, orally, can be hard to do.
Usually, plaintiffs in U.S. small claims courts are not allowed to have lawyers and are allowed to file only a certain low number of cases per year.
Software license enforcement is not an issue confined to the federal courts. And, state courts can have jurisdiction over out of state parties, so these aren't real problems.
But often small claims court cases can only be filed against defendants who reside in the county where the small claims court is located. Given that in person hearings are required, but license violations can happen anywhere in the world, this is often a serious problem.
