When Copernicus proposed the heliocentric model in 1543, its accuracy was actually inferior to Ptolemy's geocentric model—which, after more than 1400 years of refinement, had its epicycle precisely calibrated and perfectly matched the observed planetary positions.
Seventy years later, Kepler, based on Tycho Brahe's unprecedentedly precise observations, replaced Copernicus's circle with an ellipse, ultimately making the heliocentric model empirically superior.
Terence Tao's view is that science needs a high-temperature environment. If we only fund and follow the most advanced technologies of today, we will stifle ideas that may require decades to overcome their limitations.