I think you are missing my point. A dirt bike put on pavement is going to do much better than a pavement bike put on the dirt. Sure, you can take a Gold Wing on a wide/smooth dirt road, but you probably won't enjoy it that much. Instead, put dual-sport tires on a dirt-oriented bike and gear it up enough so it isn't laboring at highway speeds. You'll have a much happier time in the dirt that way. If your one bike is going to run dual-sport tires the dirt bike is going to be a better "all arounder" than the street bike.
Street bikes are probably going to be heavier, wider, have inadequate ground clearance, inadequate suspension travel and wheel-rates, too much front-end weight bias, poor foot and bar positions and possibly a lot more expensive stuff that gets broken when (not if) you fall down.
You might look at something like a DR350 Suzuki. That's an early 1990s model, but it was an aircooled single and pretty popular and reliable. I've seen them in full dual sport trim and I've also seen one that was fitted out with GS500 wheels/brakes and run on the street. It will have enough power to do freeway speeds.
Here's a couple for sale for around $2K.
1991 Suzuki DR350S STREET LEGAL
Suzuki DR350 dual sport
Or consider an XL500/600 or XT500/600 if you want something bigger for higher sustained freeway speeds.
The dirt bike can handle well on both pavement and dirt. The street bike is unlikely to be terribly happy in the dirt, or at least that should be true for what I've seen of modern street bikes. You should see about borrowing someone's street bike and try to ride it on trails, things should become a lot clearer after that.
But you should be prepared to fix the crash damage.
cheers,
Michael