That will work for new visa applications, but the problem is that Obama's State Dept. probably issued a zillion visas in the last months to anyone and everyone over there. It's a little harder to to deal with the visas that were already "approved".
My understanding of an (American issued) Visa is it allows an individual to travel from another country to America but it does not automatically guarantee entry.
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>> “It’s a little harder to to deal with the visas that were already ‘approved’.” <<
Actually, no the visas can be cancelled as an addendum to their passport in the digital system.
No problem.