It is a great idea, but NASA has rejected it for a number of reasons, only a few of which I now recall.
To briefly summarize until someone who knows the full story comes along, it goes something like this. First, the shuttle could very likely carry the main tank into orbit, but the orbit would have to be lower, or the payload weight would have to be reduced. Neither of these options were deemed acceptable to NASA.
A second proposal involved putting a small, inexpensive solid rocket onto the main tank, designed to fire after separation from the Orbiter. There are several problems with this proposal. Challenger demonstrated what can happen when a defective solid rocket burns into the main tank. At separation, the main tank is almost empty, but nevertheless is capable of exploding. Detonation of the main tank in low earth orbit could spread debris throughout that valuable orbital path, and could even endanger the Orbiter, either by the explosion itself or by passing through the debris on a later orbit.
Another problem with the “booster” proposal is that you can’t simply tack a rocket on and be done with it. Once you’ve gone to that step, you now need telemetry and guidance, possibly maneuvering rockets, a command and control system, and so on. In other words, you’ve just gone from a big dumb fuel tank to a big elaborate dumb fuel tank that has to be parked in a specific place for later retrieval.
And “elaborate” means “expensive.” Besides the Bureau of Indian Affairs, NASA is one of the most underfunded agencies in the U.S. government, considering what they do. They don’t even want to consider it for fear of diverting resources from other more important projects.
All that being said, the fuel tank to orbit proposal is one of the best unused ideas out there. The problems are not insurmountable. Raw material in space will be one of the most valuable commodities of the spacefaring future, and those giant tanks supply them in abundance. Not only could the tanks supply storage space and emergency spare parts, but the residual fuel remaining in the tanks is the most valuable part of the tank. Comprising of hydrogen and oxygen, the cargo that is currently being burned up over the Indian Ocean could supply propulsive fuel, power, breathable air, and water. When you look at it that way, is it really that difficult?