You are talking about change (or extension) of status, not visa.
US is unique in that the visa sticker and your right to remain in the country (status) are two different things. The only purpose of the visa sticker is to allow you to travel to a U.S. port of entry, where you apply for admission, and therefore legal status. You can have legal status in the U.S. while the visa sticker has expired, and your status can be changed or extended domestically. However unless you have a valid sticker you cannot leave and return.
There actually is a pilot to renew h1-b visa foils while in the US without a consular appointment.
It's not unique: Japanese system is exactly as you described.