Why would the military focus so heavily on solar power?
It's not just solar, they are also very interested in wind, geothermal/ground source, and biofuels. But they think solar and wind have the most potential for their purposes (it's mostly only the Air Force interested in biofuels, for fueling their planes).
As for why, well, 80% of the convoys run in Iraq and Afghanistan are fuel convoys. On average, a soldier died or was wounded in one of every 46 of those convoys in 2010. And by the time you take into account the cost of the fuel and the expense of moving it, the military is paying something like 5-10 times the price you pay at the pump when you fill your gas tank.
What is this fuel used for? Some of it is used to power vehicles, of course, but the vast majority of it is used to provide electricity at remote and forward bases. They dump it in a generator, burn it, and wait for another convoy. On the other hand, the sun and the wind come to many of their locations without the need for a convoy.
The upshot of all of this is that with sufficient energy densities, the military could spend a whole lot more on solar panels and wind turbines that would seem justifiable to the average homeowner and still have it be economical -- I mean, just think of the money and lives that could be saved if a base could reduce the number of convoys it needs by 80%.
For all of that, you probably don't need cells with 50% efficiency, and I guess that's why TFA focuses on soldiers' gear instead of base power.
Your concern about a soldier contending with solar panels hanging off his back is a bit misplaced, I think. TFA says that at 50% efficiency, a 10-cm square panel is all that would be needed. That is already smaller than a single standard silicon cell in production today (standard is 15-cm square). And if you're worried about bad weather, sandstorms, and distractions then I would think that the last thing you want is a mechanical device with moving parts like foot pedals.