I think the ZX6R 636cc engine is a very good engine. Overall, my bike has been low maintenance. That said, for what you're looking for, I don't think a ZX6R is the best choice.
For most people who ride on the street, there's no need for the aggressive riding position a supersport delivers. Given that you don't need that posture for aerodynamics and speed and improved COG for sharp high speed cornering, perhaps something more comfortable will actually be better. If you're more relaxed, you can ride better, longer, etc.
I have a ZX6R. But I shopped for other bikes, and still dream of not constantly shifting and bending over and leaning on my arms in traffic (really it's only a problem in traffic. Otherwise I like the bike).
I would look at
FZ1 or MT-10
Hyperstrada or Hypermotard
In the end, if there was a Z636 that was like the Z800 or Z900, I'd take it. I LOVE the power of the inline 4 and the way it's delivered from the 636cc engine. However, there's a lot more available in the used market if you look at the ZX6R; plenty of affordable bikes with lots of life left. If cost is a concern (as it was for me) the ZX6R can provide options that aren't available in some of the more rare offerings I posted above.
Never ride faster than you can stop