Also technically we vote for state electors, not the party headliners whose names appear on the presidential election ballot. The USSC cannot interfere with the constitutional mechanism used to elect the president as it is a violation of the separation of powers.
I think that is arguable. If the courts can never step in, there is no check/balance on Congress.
At this point in the contest (and it will be similar in the general), there are 50 states, all of which forbid filing a false certification of eligibility. Those laws are not federal laws, they are ballot integrity laws, and they can be enforced by state courts, as those courts see fit. If the feds want to step in and establish uniformity, they can - they can at least try.
So far, the state courts have evaded the issue, leaving the question to be decided on an individual (person) basis, as informed by public discourse.