The primary problem with leaving the tank up there is that it's to low. At typical shuttle altitudes, there's to much drag. I read some studies on it years ago, and their just isn't enough margin to make orbit with it and have it fitted out with an engine big enough to raise & maintain the orbit, attitude control, docking facilities, etc. - all the stuff you need to make it even remotely useful.
It's not some conspiracy - the physics just doesn't work out.
At point of separation from the orbiter, it was originally to be fitted with a derivative of the OMS motor
(a hypergolic Nitrogen Tetroxide/Monomethyl Hydrozine burner), metered to burn the remaining hydrogen & oxygen that was n the tank at separation -
which would have been in excess of 10,000 gallons of oxygen and 20,000 gallons of hydrogen.
It's already in motion and just below insertion velocity, just needed an ignition system to light it off after separation.
The fuel left would have boosted it to orbital speed and placed it in orbit another 50 to 75 miles higher up, within the range of the Space Shuttle's reach.
Placement of the tanks was to be a 'ring' of six connected with junction boxes to form a belt, and another six - three on each side of the belt
(think 'bicycle rim') which would joint to form offset spoke structures - tripods from the
belt, extending to the apex - one at each end.
A spin of the platform to the belt would provide some form of low grade syntehtic gravity
and the apex points would become the docking station for vehicles.
Completed configuration would have been 12 three story buildings each 150+ feet long joined into a space station structure.
The cost would have been minimal back then (late 70's) but it was abandoned as a savings to the taxpayer, an error on the cheap.