Interesting topic. One thing to consider is that exact yardage likely wasn't as important to them back then. Less consistent clubs and balls, windier conditions on the links, more shot shaping, and more ground game might have made an exact yardage less necessary, even for the best players.
If you had a 178-yard shot in the mid-1800's with a 15mph wind quartering from the right into a green with a mound in front, I'm guessing the direction/speed of the first bounce would probably be more important than the 5 yards or so of accuracy gained.
Now with the aerial game, more consistent equipment, and inland courses with little wind, I would guess exact distances are more important, at least to the elite players.
To answer your question, though, I think you're probably right that this kind of equipment would not have been allowed.