A couple of issues with your numbers. 1) you are basing yourself on average grid prices in the US and the local cost of petrol. You should instead be looking at dedicated clean energy installations that you'd be using 100% for fuel production in places where that are optimal/ideal to do so. 2) those petrol costs exclude taxation that would apply in e.g. the EU. Current prices in e.g. Germany for a liter of petrol are around 1.20 euros. Much more in e.g. the Netherlands, which taxes much more aggressively. Bottom line is that petrol is really expensive already in a lot of places and not likely to get cheaper when people are getting worried about global warming.
So, petrol is a lot more expensive in a lot of places and clean energy is a lot less expensive in a lot of places. I'd say, we have about a 3-6x margin of error here. And that's just at the current rates.
Luckily, clean energy cost is dropping rapidly and projected to continue to do so for quite some time. The EIA's estimates appear to be averages for the US in the context of grid electricity. There are already places in the world where those prices are far lower (i.e. by magnitudes) and projected to drop even further.
Solar grid prices in places like e.g. Dubai, would be something like 0.024$/kwh. That number might already be obsolete. So, well below what you seem to consider the break even point. Even at 30% efficiency (as opposed to your 100%) this is starting to look pretty feasible. The Prometheus founder seems to be suggesting 60% is the efficiency rate elsewhere in this thread.
Boom economically viable right now in Dubai. A region well known for its dependence on crude oil exports. How cheap would this have to get for them to not bother pumping oil out of the ground anymore at all? Incidentally, they are already using solar to power those pumps (burning oil/gas to do the same is already uneconomical). They could be producing petrol with that energy directly instead. You have to wonder at what point that starts making more sense and what that would do the global oil/gas markets. I think it's more a question of volumes/scale than cost.
So, this is not "an incredible engineering challenge" but a simple matter of how soon the cost lines cross and economies of scale. Depending on your point of view, this may already be cheap enough right now. The point is kind of moot because by the time production is ramped up to the point where this has meaningful impact, energy cost per kwh will have come down much further whereas crude oil and associated taxes are not anywhere near as likely to go down or even stay the same. I'm guessing ramping this up will take quite a bit of time (2-3 decades?). In the process, economies of scale, will impact the pricing some more.