I suspect LBJ did or tried.
But what did he accomplish as VP?
The most the VP could have other than that tiebreaking vote is the power to lobby. But hell, EVERY former Senator has that.
Naa, I think someone like Pence would be a good choice. Good optics, Executive experience, Legislative experience, Respected enough on the hill to be a real asset to a president with zero government experience.
The optics of two old men running on the GOP ticket are horrible, and will be viewed as trying to get in the way of America electing its first woman President.