Depends on what you mean by a huge problem.
If you are referring to energy loses due to the large distances and the electrical resistance of the wires carrying that power; you'll discover those loses are directed related to current and that you can trade current for voltage and trade voltage for current; so we can avoid losses by upping the voltage.
If you are referring to the fact that the Earth's crust is moving, we can have geologists do some work; estimate the distances spaces where we will be running our wires and put in sufficient slack to cover the time period until the next maintenance window.
If you are referring to weather event induced disruptions in the grid (wind/tornadoes/etc taking out power lines) then you build alternate paths to route around damage.
If you are referring to solar storms and coronal mass ejections, then you need standards in your equipment to deal with out of spec distribution lines.
All of which are technical problems and easy to solve.
If you are referring to the bureaucratic hellscape that is international coordination and cooperation, then yes that is the only huge problem preventing such a solution, despite its numerous global economic and environmental advantages.
well no storage can be 100% efficient but you are correct that thermal storage is very efficient if you want a thermal gradient to leverage for heating (cooling as well)
I am assuming you mean Pumped-storage hydroelectricity when you say PHES and no it also falls under F=ma, but when using the terrain is able to increase the amount of mass to a more industrial useful scale. The larger the scale the smaller the losses. Hence most economical when one has mountains for the storage of the water. (metal/plastic tanks on elevated platforms tend to be much less efficient and more expensive).
I guess it depends on what you mean by rare long duration events but yes one can imagine a situation where the burning of hydrogen is justified on an energy needs basis.