I'm not sure you need a 'breakthrough', just many incremental improvements will do the trick.
We are also getting better at producing cheap power. For example thanks to intermittent sources like solar and wind, in many places electricity often becomes free in wholesale markets some times of the day.
AI generation (including video) currently takes at least a second, and users expect that delay. So that means inference is not latency sensitive and you can put these data centres anywhere in the world, wherever power is cheapest. Model training cares even less about latency.
At the moment, the hardware itself is too expensive (and nvidia has long backlogs), so people run them even when power is expensive. But you can easily imagine an alternative future where power never becomes cheaper than today (on average), but we have lots of AI data centres lying in wait around the world and only kicking into full gear when and where power is essentially free.
We are not getting better at producing cheaper power as the cost has increased per hour a lot over the last 50 years. But we are generating more power from different sources that are cleaner.
Power needs to be given away or people paid to take it is more of a function of limited storage abilities and limited ability to scale down rather then generating unlimited power. The free power is an issue with how the system is built (and the type of power source) rather than a sign of success. The same area has to import power at higher costs when the sun or wind isn't as powerful.
> Power needs to be given away or people paid to take it is more of a function of limited storage abilities and limited ability to scale down rather then generating unlimited power.
There's no need to scale down solar or wind power.
Yes, storage is another way to make money from power prices that differ over time.
> [...] the cost has increased per hour a lot over the last 50 years.
Some sources of power, like solar, have been dropping in price a lot recently.