But we were discussing transportation usage, not grid storage.
Batteries don't make sense for seasonal grid storage, so you will need some other mechanism for storing and using energy. But you do have the factor that A/C use is highest when you have abundant solar energy, which helps reduce the seasonal imbalance between supply and demand. And a workable storage solution today is pumped hydro - Norway alone stores around 86.5 TWh in our hydro reservoirs, and a meaningful amount of this can be used for pumped hydro.
But I see validity in the argument that some energy will be stored in chemical fuels. Short term, that will likely be hydrogen, which is then added to the natural gas network. (Something like 5% can be added without much problems with hydrogen embrittlement.) Longer term I assume the natural gas network will be gone, and some other chemical storage will be needed. Making fuel for the BFR is one mechanism for putting the energy to good use. Short range airplanes will likely be battery electric, but I think long range airplanes are unsolvable for the foreseeable future. Same with long range shipping.
So yes, we will likely have synthetic transportation fuel. But not for road going vehicles. Road going vehicles use so much energy that there isn't enough "surplus energy" to meet the demand, and road transportation is low hanging fruit for electrification.