The Cavendish experiment was really an effort to calculate the constant in Newton's Law of Gravity. ("Big G") You can't easily work it out without knowing the masses of the objects involved - which is hard to figure out for stars, planets, moons, etc. Hence Cavendish (and others who refined his experiment) use known masses so they can figure out 'G' directly rather than from 'g and guesstimated masses for planets and such. We don't need Cavendish to explain how gravity works - that can be deduced by watching the motion of planets in a heliocentric solar system.
Sure, but that's not why it's important in this context. In this thread we are not anywhere near any G yet, big or small. We could go faster, but the people here love their hair thoroughly splitted.
EDIT: you work with too many assumptions. Newton assumed a 'RE. "No shit sherlock" you are probably saying, but that's precisely the problem 
Well, he famously said: "If I have seen further, it is by standing on the shoulders of giants."
He stood on the shoulders of Da Vinci, Galileo, Copernicus and others. They proved the heliocentric model...which depends on the earth being round.
But by the 1650's there had been enough circumnavigations and other long distance ocean travel using only "star and compass" navigation that any rational doubt as to the shape and size of the earth had been completely answered.
It's entirely unreasonable to expect every new generation of scientists to re-prove things that are already well established...just as you no longer have to convince yourself that apples are not poisonous before you eat one. There are things that are just so well established that they can't be wrong.
Unless, of course, you're a Flat Earther.