Yes that's usually called "death by snu snu" after it was popularized by an episode of Futurama. It's actually quite a popular fetish and is one of the reasons why there are so many Japanese hentai games centered around it.
Getting milked to death one way or another is something i actually wished existed in this game. It doesn't have to be with every girl or every scene obviously but i wish Koda and Bo tried to diversify things more. There is an overwhelming amount of foot scenes in these game... while many of the other fetishes get ignored, even though they all fall under femdom.
I'd be really surprised if it wasn't a thing before Futurama. I loved the series and I like the trope, but I found the episode more funny than sexy. I think the main reason it's so popular (or at least why it resonates for me), is because of the context. For instance while normally I might prefer a footjob scene to a vanilla sex scene, as someone mainly attracted to femdom, if I had to choose between a missionary scene where the woman led you by the nose over and a footjob scene where she's doing it because she wants to satisfy your foot fetish while she's clearly uncomfortable, I'd take the former in a heartbeat.
Having the woman milk you to death, no matter how she does it, is pretty much the epitome of femdom, it shows she only cares for herself and her pleasure. And if you end up wanting it yourself it makes it even better in my view. You're practically saying that you find her so sexy that there's nothing you wouldn't do to enjoy being with her a little longer, which is one of the best compliments you can give.