Lots of countries have temporary worker status. The requirement to leave the country to re-up it appears to be a distinctively American thing.
I was recently in Malaysia on a digital nomad visa. When it expired I was required to leave the country and either wait for the renewal to go through or reenter on a tourist visa (and either not work or work illegally). So not distinctively American.
It's definitely not. I know Japan and Korea had a similar process when I was living there, and I was under the impression that most places operate this way. Your visa grants you right to temporarily stay in the country, and if you don't have a visa you have no right to be there. Sometimes there's a bridging visa to cover the gap, but a country isn't under any obligation to provide one.
I've renewed my visa in Japan a bunch of times, including changing work category or visa status, and never had to leave the country for it. It's not standard for working or student visas, though you would have to leave if you were switching from a tourist visa to a different category.
But my point is it’s a known factor up front, and it’s so they can (have the option of) getting you to leave without allowing you back in. The thinking is that if people had visas that expires or revoked, they just wouldn’t leave and enforcement would be difficult (we have a forceful ICE now, but not always). Having them leave first is by design even if unique.
It’s fairly common in destinations for migration, less so elsewhere.