Wasn't it solid state hard drives replacing those spinning disc that made a big jump forward? Aren't a lot of our memory sticks of a solid state technology??
Bell Labs introduced the solid state transistor in the fifties. Spinning drive technology( ferromagnetic storage) was developed after that ( I believe Winchesters start showing up in the seventies). Hard drives are still used ,the cost per byte storage is still cheaper than flash , last time I checked and silicon wafer space is running out , IBM was exploring going to 3D wafers to increase capacity.
You usually need several molecules to make a transistor to store a bit. Theoretically ,Ferromagnetic ( Spinning drive )you only need to orient one molecule to store a bit( you could store more per molecule if you can control the oreitation accurately enough) . Flash, right now ,is just faster access wise .Spinning Nano machine hard drives could become a reality.
The research in to batteries is not necessarily to make a better battery but to make a cheaper or safer battery . Battery technology is reaching its limits .Lithium is the lightest metal on periodic table so they usually make the lightest batteries for a given energy density ( watt hours/kg ) . When it comes to life expectancy NiCd is still the king (I have several NiCds that are well in excess of 10 years)
One of the biggest problems with Li ion battery technology is safety , Lithium self ignites at room temperature when exposed to Oxygen (O2). It will burn faster when exposed to water (like from a firetruck trying to put the fire out) . Lithium will rip the O2 right off the H2O molecule . All that has to happen is the membrane gets punctured . If they are charged incorrectly they can out gas and burst the membrane causing a fire to start.
Aluminum Ion has almost as many problems , Aluminum just doesn't burn when exposed to Oxygen or water,making it a little safer.
For large power requirements the future lies in fuel cell ,direct conversion of "fuel" into electrical energy. Where "fuel" is chemically stored energy preferably in a stable liquid form .
https://en.wikipedia.org/wiki/Type_212_submarine