What's so ridiculous about this? There's dozens of potential battery chemistries which could do this - sodium ion, lithium air, nickel lithium, lithium sulfur, and on and on. The payoff for all fields could be incredible. Why not have an organized program to work on it? High cost, high risk, high reward - the kind of basic research that's perfect for government programs (leaving the incremental tweaking, production optimization, marketing, etc to private industry).
To give an example let's pick one field - transportation. What does "5x energy density and 1/5th the price" mean for transportation?
Current energy densities generally provide EV ranges between 100 and 250 miles. 5x - 500 to 1250 miles driving per charge. Which means a single charge provides a full day of charging. Which means that it doesn't matter how fast you can charge, so long as you can get a full charge when you sleep.
Let's go with 800 miles range. Which would be extended if you plugged in during meals and/or breaks. A car with prius-level streamlining will use about 250 watt hours per mile on the highway. That's a 125kWh pack. With 80% net wall-to-wheel efficiency, you need to provide about 156kWh. Over 8 hours, that's 20kW, or about 80A. Most new homes have in the ballpark of 200A boxes and worst case, you upgrade.
In short, these kind of batteries would entirely eliminate the main two complaint about EVs: range and charge time.
What about price? Li-ions are roughly $200 per kWh nowadays, which would make that pack. That's $25k just for your pack's cells - pretty darned pricey! Now, contrary to popular myth, these packs are generally rated for a decade or so to get down to 80% capacity, and the bigger your pack, the less you stress your cells, so they're not a high-replacement item (there's even a potential aftermarket for used packs). But that's a ton of money. However, $5k for the cells would be a *dramatic* improvement, and quite realistic when you consider how much it simplifies the rest of your vehicle.
All of this would come with a whole range of other benefits. You'd never have to go to a gas station again. Your fuel would cost a small fraction as much as gasoline. Your maintenance would be way lower. Even your brakes would wear down slower (regen). If smart grid features take off, you could make money by simply leaving your vehicle plugged in. Increasing vehicle power is comparatively very cheap versus gasoline and actually *increases* your vehicle's efficiency slightly (fatter conductors to handle the higher peaks = lower losses at under normal driving conditions). On and on and on.