One important function of the double bottom tank is structural strength. The first ship to be fitted with double bottom tanks was Brunel's S.S. Great Britain and she went aground on the Irish Coast on her maiden voyage and survived intact for a year before she was salvaged, and she is still with us in drydock at Bristol.
The longitudinal strength of a ship can be viewed as a Box girder, the ships sides, deck and bottom make one box girder, the double bottoms make a 2nd Box girder and the cargo /Machinery spaces make a 3rd. If wing tanks are fitted these make an additional 2 box girders, and greatly improve longitudinal strength.
The double bottom and wing tanks can be stiffened with transverse floors and longitudinals in a way that would be impractical in machinery or dry cargo spaces and impossible to clean in cargo tanks.
One of the advantages of a double hulled tanker design is that the frames can be put in the wing and double bottom tanks, making draining/ stripping of cargo quicker and easier and also facilitating tank washing.
Some tanker designs even have the frames for the deck plating on deck rather than inside the tank.
I wouldn't be worried too much about pollution from oil in double bottom tanks, oil floats on top of sea water, and unless the tanks are completely full or the ship eventuall breaks up, little oil will be lost.
There was a very cogent arguement put forward for designing tankers on this principal rather than adopting double hulls, but it required a basic level of technical comprehension to understand, so it was far beyond any Politician's comprehension.
It is always better to ask a stupid question than to do a stupid thing.