Let’s assume that stablecoin usage grows massively. Everyone everywhere has easy access. 

People in countries where the currency is less trusted will move lots of money to stables. 

What happens when these less trusted countries lose control over their local currency?

This is a good question but the answer is most countries haven't had a functioning fiat currency ever. Many fund what little projects they can on external financing via IMF or China, and that funding only goes to infrastructure and real estate projects.

Less trusted countries don't have rule of law for anyone to use their currencies, hence why they're less trusted to begin with. Their citizens consistently dump the local currencies and the bond market never trusts loans in that currency for a reason.