I think you're missing something. If you're talking about tourists, after the first 60 days, and extending once for 30 days more, a border run is the only option if they want to stay any longer. I don't think most people would do a border run just after the first 60 days.
You can't be visa exempt and visa holder at the same time. As long as your DTV is valid, you'll always enter using it, even if you don't mention or say anything.
Some embassies require you to be a resident. I applied in Seoul, Korea and at least at that time (August 2024), only residents were allowed to apply. In Tokyo, Japan, the same. They might have since relaxed the rules or not, but the thing is this is Embassy-specific, so it's better to ask before applying in case you're not a resident, except in countries where is well known that anybody can apply, such as Laos, Vietnam, Indonesia, etc.