So for those that don't know, it's quite common for a visa renewal to be required to leave the country. Depending on the visa, you might have to do this every year. So just imagine, having a normal job in the US and you're asked to leave to renew your visa and this stuff happens. That's no more appointment, not even a new date and you're now very likely unable to work and possibly can't even enter the country to get…
You are confusing some terms. You are never asked to leave to renew the visa. Visa is an entry document. It only serves the purpose of granting you entry. When you are in the US, your stay is covered by your status. If you extend or change your status, you will continue to be in legal status in the US. That is, you are never asked to leave as long as you are in status. If you do leave on your own though, you will need a new visa if your old one has expired. So the TLDR is that if you leave on your own, you will get stranded.