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.

It's not unique: Japanese system is exactly as you described.

There actually is a pilot to renew h1-b visa foils while in the US without a consular appointment.

Similar even with LPR (Legal Permanent Resident) status. Your green card is valid for ten years. When the card expires it must be renewed, but your status does not expire. But you would need a current, valid card, to re-enter if you left (or have extenuating circumstances which you'd -reallllly- want to have worked through with a consulate prior to attempting.

I thought that was universal. The Visa gets you into the country. Your entry stamp shows how long you can stay. It was an extra white card in USA but I forget what designation the form had. Been a while.