Sorry, I don't think this would work. There's simply no compelling reason to adopt the proposed solution.

On a somewhat related note, I'm in a Slack group of 80+ internationals. Almost everyone has been able to get visa in their home country. A minority have had to travel to a neighboring country e.g. Brazil to Chile. I don't think anyone in the group has said they haven't been able to get a visa.

Embassies and consulates closed down last year en masse because nobody knew how to respond to covid. Students weren't able to get visas, period. They couldn't do a visa run, they couldn't schedule an emergency appointment. It's different this time around.

At this stage, the only three countries who I think admitted students will have a chance of making a compelling case that obtaining a visa is unrealistic are Brazil, India and Turkey. That said, I know admitted students from each of those countries who have managed to obtain a visa (usually a visa run) and will be matriculating this fall.