Note that the viol family is extinct, moved towards a fretless version.

Not sure what you mean by this. The viol (viola da gamba) family is not extinct, and modern viols still have frets. Granted, they're not quite as popular as the violin family.

Try this: Tune your guitar. Play an open D and an F# on the high E string at the same time. Mess around with the tuning of the D; go a little sharp and flat. Just slightly. Stop when you find the "best sound", then check to see if you're still in tune.

I'm not seeing your point. I don't need to adjust anything. It sounds fine and in-tune from the beginning, and my digital tuner agrees. If you're talking about some micro-degrees of intonation that virtually no one can perceive, then, ok. But again, that's an academic problem, not a practical one. You're the first person I've ever heard complain about guitars being structurally incapable of being in tune due to their frets.