The uranium-lead transition isn’t the only one used. There’s also the rubidium-strontium transition (with a half-life of 49 billion years), the potassium-argon decay (1.3 billion years), and a handful of others. The key in all these cases is to have a rock — meteorite or otherwise — with enough atoms of the given types to perform measurements. One we don’t see in the list is “carbon dating”: carbon-14 has a half-life of about 5,700 years, so it’s useful for archaeology and dating the remains of animals from the relatively recent past, but utterly useless for measuring the age of Earth.
But why is a random process like radioactive decay useful as a clock?