Agreed there is nothing, but what it does mean is that you can make very low impedance pickups (with a very low output), which means that you aren't choking your own frequencies with the pickup, which is what EMGs do. They are active because not only would the noise be an issue, even with 6" of shielded cable, but there would be no point using them without a preamp as the signal would be too small, so might as well put one there.
Agreed - active has nothing to do with tone circuits, its just that if you have gone to the trouble of making it active, might as well make a tone circuit. Most of my basses are active, I rarely touch the EQ on the bass. In fact, nowadays that I play on a wireless all the time, there is little point me using an active, as I am already buffered by the wireless, hence most of the time I am using my Ric.