This answer is based on the two Sailor Moon Crystal seasons and fan wiki information that I found online. I may edit this in the future, if I ever get to reading the original manga or otherwise come across new information.
The prior incarnations of the Sailor Senshi (i.e. those that came prior to the "present day" of the series) were indeed born on their respective planets. From the wiki:
Act 41 of the manga reveals the Sailor Senshi as princesses of the Solar System. Each one had her own castle, which she can call upon late in the series for power. This act first enables Sailor Moon to transform into Eternal Sailor Moon. The castles are named after moons, except for Mercury's and Venus'. Venus' castle is introduced long before the others', in the Sailor V manga, but she never mentions this to them.
This is supported somewhat by the Mugen arc of Sailor Moon Crystal, in which we learn that the Outer Senshi (as their previous incarnations) simply watched over the Solar System from afar, on their own planets.
From this, it is not immediately obvious why the current incarnations of the Sailor Senshi show up as human girls on Earth. However, I think that from an in-universe perspective, there are two possible explanations:
It is now the Earth where the Senshi need to fight the various villians that show up, and that it thus makes sense for the Senshi to be there.
The other planets are no longer populated, so it does not make sense for the Sailor Senshi to be reincarnated there.