"It may be well to reply to the very natural question: What would be the use of such extreme refinement in the science of measurement? Very briefly and in general terms the answer would be that in this direction the greater part of all future discovery must lie. The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote. Nevertheless, it has been found that there are apparent exceptions to most of these laws, and this is particularly true when the observations are pushed to a limit, i.e., whenever the circumstances of experiment are such that extreme cases can be examined. Such examination almost surely leads, not to the overthrow of the law, but to the discovery of other facts and laws whose action produces the apparent exceptions.

As instances of such discoveries, which are in most cases due to the increasing order of accuracy made possible by improvements in measuring instruments, may be mentioned: first, the departure of actual gases from the simple laws of the so-called perfect gas, one of the practical results being the liquefaction of air and all known gases; second, the discovery of the velocity of light by astronomical means, depending on the accuracy of telescopes and of astronomical clocks; third, the determination of distances of stars and the orbits of double stars, which depend on measurements of the order of accuracy of one-tenth of a second—an angle which may be represented as that which a pin's head subtends at a distance of a mile. But perhaps the most striking of such instances are the discovery of a new planet by observations of the small irregularities noticed by Leverier in the motions of the planet Uranus, and the more recent brilliant discovery by Lord Rayleigh of a new element in the atmosphere through the minute but unexplained anomalies found in weighing a given volume of nitrogen. Many instances might be cited, but these will suffice to justify the statement that "our future discoveries must be looked for in the sixth place of decimals." It follows that every means which facilitates accuracy in measurement is a possible factor in a future discovery, and this will, I trust, be a sufficient excuse for bringing to your notice the various methods and results which form the subject matter of these lectures."

Light Waves and Their Uses. By Albert A. Michelson. Published by The University of Chicago Press, 1903, pp 23-25.

Michelson was arguing exactly the opposite of the position you imply. In context, "the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote" is referring to the fact that new physics (e.g. relativity) tends not to invalidate the older physics which approximate it (e.g. newtonian dynamics) in common situations.

He was arguing that the all the important and fundamental laws of physics had been discovered. And so all that remained was to work out what was causing perturbations at increasingly esoteric degrees of precision. In other words that the future of science rested on refining previous discoveries, instead of the discovery of new revolutionary concepts. In the words of our OP here that, "all the science that is possible to do "at home" [is] already done."

Yet of course he made these comments just before physics would be completely revolutionized, and rapidly lead to revolutions in life as we know it. This was prior to relativity, prior to quantum mechanics, even prior to atomic models. The thing that makes it utterly ironic is making such comments at such a time after being an inadvertent key player in the discoveries to come.

Quantum theory didn't completely overrule how physics works at large length scales. Relativity didn't completely overrule how physics works at slow speeds & sub-planetary length scales. These are the 'apparent exceptions' to the laws of physics Michelson refers to, which lead to 'the discovery of other facts and laws whose action produces the apparent exceptions'. Validating both of those required 'extreme refinement in the science of measurement'. Look, for instance, at the 50 year effort required to validate the Bell Experiment.

Michelson further backs up this point in the next paragraph, where he provides several examples where precise measurements similarly lead to new science. Even more, look at his call to action: "Every means which facilitates accuracy in measurement is a possible factor in a future discovery".

His argument isn't dismissive of new science because it only leads to small differences in measurement. It's supportive of small measurements because it's required for new science.