A global grid would be an immense coordination problem with tremendous costs. Some form of storage local to each grid is likely to be more cost effective. There are so many storage options, something should be appropriate as the need becomes real: pumped hydro / other mechanical, battery, synthgas (maybe), heat, pressure.
Repeat that cable 9.6 times over 3,459 miles from London to New York would be 66% efficient and cost €5.8b.
If energy is $0.05/kwh in London and you can sell it around the retail rate of $0.12/kwh in New York, your cable will make around $20k/hour ($0.028/kwh,after cable losses). Your cable will pay for itself after 33 years of complete capacity saturation.
With free energy at one side and retail prices on the other, the payoff time narrows to less than 8 years.
This calculation leaves out so much but it was a fun thought experiment.
May I add a proposal to convert the mediteranian sea into a pumped hydro storage with long-term capabilities? It would need the same dam as the Atlantropa, but possibly less extreme.
There are some basins around northern Africa that might be amenable to slight terraforming, or just a re-activation of Operation Plowshare to blow a cavern which has it's rubble content lifted out and then used for subsurface pumped hydro.
Alternatively plan to collapse the cavern roof into itself after filtering persistent radionuclides and waiting for short half-life isotopes to decay. Collapse via conventional quarry techniques (a circle of drilled wells filled with ANFO?) or iteratively with robots that go out towards the center and drill to blast this off somewhat continuously. Then use a nearby water reservoir to pump in-between. Salt content shouldn't matter much except corrosion protection techniques.