It's literally exactly the argument.

If teachers were underpaid - it would be a poor argument.

But if there's an acute shortage of 'key' workers in jobs that require education, for jobs where wages are materially above market pricing - then this is where you want H1B type programs.

The idea is that it should not harm the local market for labour, and it's usually not reasonable to expect market wages to be a radical departure from where they would be otherwise.

Aka - if teachers are earning $80K on average, then it's not going to work out i some small towns need to pay $150K to bring people in from the city, it also creates problems for locals.

Special worker programs can be well utilized here in the right circumstances.

The 'bad' scenario is when labour market is flooded where those jobs would otherwise go to locals.

Tata/Infosys (generic IT workers) are alone probably 80% of the problem.

This would hold more weight if teachers in rural areas weren't getting paid less than half your thought experiment average.

Teachers are underpaid. No occupation paying under median wage in the area should be granted work visa.