Haven’t heard of forever sauce but my family makes sauce by cooking it pretty much all day. If we ate it every day then yeah we might as well keep a pot on the stove all the time
If you cook the tomato too long you lose the tomato flavor[1]. My Italian-American neighborhood has a sauce competition at the community center every year, and the winners never do an all day cook.
[1] https://www.seriouseats.com/the-best-slow-cooked-italian-ame...