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That only worked for sedimentary rocks, and only some of those.
Rocks of Precambrian age had only the rarest wisps of fossils.
The other method relies on actually counting the atoms of each isotope, not waiting for some of them to decay. It involves preparing samples and running them through a mass spectrometer, which sifts them atom by atom according to weight as neatly as one of those coin-sorting machines.
The geologic equivalent of lighting the grill is the time at which a mineral grain solidified, whether that is long ago in an ancient granite or just today in a fresh lava flow.
The solid mineral grain traps the radioactive atoms and their decay products, helping to ensure accurate results.
A hundred years ago, our ideas about the ages of rocks and the age of the Earth were vague. Judging from the amount of rocks there are, plus the imperceptible rates of the processes forming them—erosion, burial, fossilization, uplift—the geologic record must represent untold millions of years of time.
It is that insight, first expressed in 1785, that made James Hutton the father of geology.
In 1896, Henri Becquerel's accidental discovery of radioactivity showed what might be possible.