Re: The storage is there, as advertised.
>>Sometimes I look at the modern world and despair over the sheer waste ...<<
But in CS theory, you must have an infinite amount of memory (that's flat memory, no hierarchies of registers, cache, RAM, disk, etc all those are an implementation issue) to do all computable problems. This is the Turing model.
Some computable problems will fail because you run out of memory, others because you run out of time (intractable), and still other problems are impossible. Computing tends to stick to easy, tractable problems.
Ref: Algorithmics, The Spirit of Computing by David Harel.