It's not exactly what you're talking about but there's a post degree completion extension for F-1 visas, and extension for that for masters/doctoral students th

It's not exactly what you're talking about but there's a post degree completion extension for F-1 visas, and extension for that for masters/doctoral students that can extend the visa (iirc) for up to three years and allow one to work. I've known several people that transitioned from their F-1 OTP to H1-B. I've even known people who sought out masters programs to extend their student visa just to avoid returning to their home country due to political turmoil and violence. But that said, you would make it more difficult for American citizens to attend American graduate degree programs that they subsidize with their taxes. There's a finite number of seats for students and I'm not sure if they're better filled with locals or people who want guaranteed permanent residency.