Wrong. The Mr.Gutsy and Mr.Handy models are prewar tech, and they hover.
They were first created in the 2040 I think. While slow, it's not unlikely that the technology was enhanced in the following years for daily use such a hoverbikes and such
Okay, you have hovering robots, I'll give you that. But I've never come across any wrecked cars or cycles that looked like they hovered.
My opinion still stands on this, though. I think a hovercycle might be a good idea for a videogame in general. I still don't think it's a good fit for a Fallout game, however. It still feels like a bit too high-tech for something the player would be able to get his hands on and make regular use of.
I don't know, maybe if you have a large number of possible vehicles you could eventually tinker with and get running, and one of them was a fancy hoverbike and it was a part of a high-level sidequest to find it I think that would be okay. Like if you start out with a bike that you could hardly keep running for long enough of a stretch to make it worthwhile. Then you eventually find a car that someone has managed to cobble together. And you keep finding upgrades and better vehicles, and eventually you can find a rare hovercraft so that you really appreciate how high-tech it is. That would work, I think.