I feel like the sheer amount of space at the Hearn is daunting, and it will require probably some major capital and likely some government involvement to make it work.
IMO in its current state and context, to create something like the Tate means that the Hearn would almost be closer to the Getty- a project willed out of thin air by a billionaire that can provide it enough of a critical mass of programs and a collection that can draw in visitors in an isolated environment, as well as the infrastructure to get these visitors there and amenities to keep them comfortable enough.
The movie studio scheme made sense, but at the same time its current industrial condition probably offered more potential than as sound-stages, of which there are probably easier conversions and better spaces available.
For now, its potential is precluded by its enormity, isolation, and poor local infrastructure (Unwin Street is still post-industrial), but I'm sure we will eventually get something there as the 'civilized' edge of the city creeps closer with the completion of the infrastructure works around the Lower Don.