Here in Australia we conform to a standard called MEN or multiple-earthed neutral, which means that an earth stake is hard wired to the neutral conductor at both the transformer and the residence, the reason why in an AC system we refer to one conductor as neutral comes more from the 3 phase delivery of it,
To the left of the image is called a delta topology, (415V per phase), and on the right is Star (240V to neutral and 415V phase - phase) which you would be more familiar with, and if you wanted to redefine your active as your neutral, have a think on what happens to those other 2 phases?
Even if your house only connects to a single phase, they still deliver it over 3 on the power lines out the front of your house, and they even try there best to balance the loads per phase between houses, as it means less current flows in the neutral conductor, (practically 0 current flows down the neutral wire when all 3 phase loads are balanced)
getting back on subject, the MEN approach was so that if you have a ground stake fault, you still have the neutral conductor to carry the current, and in a worse case, if the neutral wire fails, the current only needs to flow to your nearest neighbors stakes, rather than the hundreds of meters the transformer is located at, if you measure your ground connection with a clamp ammeter you may even find some current flowing into your (current takes all paths),
To answer the other implied question, floating the system can cause problems, as both mineral content, various leakages from underground wiring and static charge in clouds above you can shift your plot of dirt's potential up to a few thousand volt, from a fixed reference, and this can result in easily fatal equalization currents if you happen to form a path between the 2 (think of the mains conductors as a big capacitor, and the earth as a big capacitor, and you as a crowbar connecting a flat capacitor to a highly charged one)