How else would Cruz evidence his citizenship? If you don’t have a U.S. birth certificate, it stands to reason that you have to have another document of some sort evidence your citizenship.
It isn't up to Ted Cruz to prove his citizenship. That's his natural condition, and he and others will attest to it with sworn affidavits. That's the way it works.
You don't believe he's Constitutionally qualified? Don't vote for him. Simple.