No, the main reason was that they knew the first few launches would be out in the weather a LONG time... there would be inevitable problems that cropped up and they would take longer to fix since everything was new and untried (and the folks working on it didn't have experience with those particular problems to streamline the process). That would all add up to much longer pad times than was anticipated for "regular" shuttle flights once the program got going.
Sun particularly does pretty nasty things to unprotected spray-on foam... if you're ever at Cape Canaveral Air Force Station and have a chance to go to the rocket garden out there and go underneath the Delta IV core they have out there, you'll see what I mean. The Delta IV is covered with a similar type of spray-on foam insulation and it's VERY porous and brittle... the outer layer of bubbles tends to "pop" after a while, opening the foam up to more exposure... there are all kinds of handprints and fingerprints in the foam because it becomes very soft and "mushy" from exposure (this core has been there a long time-- it was a test article used for fitment and integration tests for Delta IV's pad and GSE when it was first coming online a decade or so ago). The foam eventually flakes away bit by bit until its gone... anything touching it merely accelerates the process, as more and more is directly exposed to the elements as the outer layers are blown away...
The other reason was that the white paint gave a very good visual indicator of the heat loads on various areas of the tank. If you look at ET jettison pics from those first couple missions, you'll notice the paint is burned in a distinct pattern on the surface of the tank-- the ogive "nose cone" of the ET itself gets significant aero-heating, as well as the areas of the ET adjacent to the nose caps of the SRB's and the orbiter itself, where the shock waves from the nosecaps impinge on the surface of the tank, and of course the exhaust plume recirculation at the base of the ET where hot exhaust gases from the rockets are drawn back up into the low pressure area under the ET in flight, roasting the base of the tank... All this was aeromodeled of course in the computer, but the paint burns and photography acted as a direct verification through experience...
Once that was accomplished, there was no real reason to go to the additional expense of the paint itself and paying folks to apply it, only to have to carry an additional 600 pounds of dead weight which detracted directly from payload capability to orbit. Deleting the paint therefore saved the money of the paint, the cost in man-hours to apply it, and saved that weight for additional cargo capability... win/win/win...
Later! OL JR
PS. As someone mentioned, the tanks had been shedding foam and causing problems from the very beginning-- and NASA knew about it... it was one of those 'normal deviations' that they ASSUMED could never bite them (until Columbia broke up and seven astronauts were killed... AGAIN)