Put a few nukes on the Shuttle, and you can drop them anywhere in the world with much less warning time than intercontinental ballistic missiles. At least that's what I read about the reasoning of the Russians building their own shuttle, because when they ran the numbers on the Space Shuttle they concluded that a "civilian use" didn't make much sense.
Cargo capacity... Not that much really, since you're carrying yourself a whole lot of orbiter already. It had a large volume in the cargo bay, and the mentioned ability to retrieve things in that cargo bay.
But yes, DoD/military influenced the design of the Shuttle. It just turns out they never used the capabilities they requested. And so you end up with a craft that makes little sense for civilian use, except for the building of a massive space station in orbit and eventual servicing of satellites.
Consider that a large number of Shuttle missions were classified, then put two and two together...
Rather than nukes, I always thought the main advantage of the Shuttle was the ability to bring things back to Earth. Which it did, a few times:
* https://en.wikipedia.org/wiki/STS-32
* https://en.wikipedia.org/wiki/STS-51-A
* https://en.wikipedia.org/wiki/STS-57
* https://en.wikipedia.org/wiki/STS-72
When then Shuttle was proposed, this was one of the main selling points. Having used it just 4 times over 133 missions... Well, that's not what was envisioned.