The problem is that the sources like solar have both power density and availability problems in higher latitudes, and power density required to e.g. power a major factory may be a problem even in a sunny place.
I'm also not sure about price per kW of installed generating power; it looks like solar power is still way behind atomic power in this regard.
In general, everyone would love breakthroughs both in electricity generation, transmission, and accumulation. Looking at the amounts of coal still mined for burning, generation should not be overlooked.
Fusion: By '24/7' you mean the 0.5 s sustained burn at JET in the 90s. Humanity has not yet managed to sustain fusion for a full second on the Earth, let alone get any useful power out of it. ITER (the next generation Tokamak test reactor) isn't built yet. The intent is for it to achieve 1000 s of fusion burn time. Its over budget and behind time, and they've just had a management reshuffle to try and deal with this.
* Edited & extended to try and incorporate nbouscal's feedback from below
The Helion design which Ycombinator funds is pulsed, so sustained burn time isn't applicable. It's also much smaller and cheaper than mainstream tokamaks.
[1]: https://en.wikipedia.org/wiki/Illusion_of_transparency
Edit: +1, much clearer what you mean now.
Electric power can probably be used to synthesize traditional fuels from carbon dioxide and water, to stay carbon-neutral. Plants can do that but in a quite inefficient manner. A (bio)chemistry breakthrough is badly wanted on this front.
Lithium-ion batteries are still at least $100/kWh (probably more like $300/kWh) and assuming a useful life of 1000 charge/discharge cycles, you're talking between $0.10 and $0.30/kWh just for the STORAGE! That doesn't even take into account the cost of generating the energy to begin with, nor the losses that come with charging and discharging the battery, nor the capital cost on the inverter that absolutely isn't free and definitely doesn't last forever.
Until storage can be had for a few cents per kWh storage is an unsolved problem.
I suspect that it will continue to be an unsolved problem for quite some time. Not because it's impossibly hard, but because getting oil or gas or coal out of the ground is so easy and has such large energy gain (output energy / input energy) that you have to be very clever to beat it.