Well you just made my point perfectly. But the increased accuracy of measure was brought by the need to explain, not the other way.<quoted text>
Not just. For example, the heat capacity of gases is determined by quantum effects and the classical treament simply failed.
The plum pudding model of the atom, which was required by classical descriptions of electromagnetism, was shown wrong by Rutherford's experiments. That required a complete restructuring of the way atoms work.
The Michelson-Morley experiment attempted to find the motion of the earth through the ether, which would have been detectable if Newtonian physics was correct. But that next decimal point showed that the classical description was wrong and so relativity was required.
The problem is that the models were working quite well at some level of approximation, but not at the next level. Adding a decimal point required a complete change in the underlying theories.
Which was my point, that our ability to measure is our strong point
in science, that does improve. I suppose it may be hasty to say 1 second error in 3.7 billion years is near absolute, this could be improved to 1 second in 7 billion, or 1 sec in 14 billion, but reveling the accuracy now is not all that arrogant.