Why cannot machines use energy stored in a way similar to biological systems' energy storage?
The activation energy of breaking these covalent bonds is high. Biological systems use phosphorylases to couple ATP to glycogen such that the high energy phosphate bonds then supply some of their energy to break the covalent glycosidic bonds in glycogen 

So problem 1, high activation energy.

Secondly, how are you going to store the energy in the machine? Conventional electrochemical cells use something like what was written about membrane potential. Their energy is accessible as it is in a form of an electrical potential. When you expend energy to break storage molecules into glucose, there's not much for you to do on the glucose other than to burn it. Burning it is extremely inefficient and makes up a huge amount of energy loss to wasted heat. The other way would be to oxidize it. You'll need something to accept the electrons (NADH and FADH in biological systems), something to overcome the high activation energy of oxidizing the bonds at every stage (more ATP coupling), something to harness the high-energy electrons from glucose (electron transport chain/chemiosmosis). In all, it is too complicated to be replicated efficiently.

So problem 2, there are many complicated steps involved.

This is why only simpler versions of the above exist. Power to gas shows us the splitting of H2O into H2 and O2. This is akin to only one stage of bond-breakage in respiration, and is simple enough to carry out (through electrolysis). H2O donates and another H2O accepts the electron. Energy is supplied as a electrical potential in the circuit instead of ATP coupling from enzymes.

Last problem is, there really isn't a need to store energy in other forms than an already-existing energy storage molecule. Most of our energy storage is in the form of carbon compounds, and electricity. Carbon compounds are high energy density, and electricity is easy to manipulate. It is perhaps trivial to the world to attempt condensing table sugar (glucose) into starch. It is not efficient enough to be impactful. Biological systems need to do this because storage is on a scale comparable to the cell body, and directly relates to survival. High blood glucose in animals might lead to hyperglycemia, triose phosphate (product of respiration) is used for lipid formation and in turn building of cell membranes, glucose molecules are used as monomers in the production of cellulose, aka cell wall in plants, (a heck ton of other metabolic pathways exist), etc.

This link shows us the different ways of energy storage in our world. We're not limited by biological constraints, so even compressing H2 into a liquid, will be more efficient than interconverting that into other forms of chemical energy, if you're talking about for pure "storage"'s sake.

I highly recommend reading up on photosynthesis, to see how biological systems harness energy from the sun, and store that into covalent bonds between CO2 molecules. More specifically you can look up Krebs Cycle.