Going from memory here, (but, see this page at Encyclopedia Astronautica)...

Dyna-Soar was Air Force, and I recall its mission being manned reconnaissance. I also recall the timing as being soon after the Soviets shot down a U2 -- the X20, if commissioned as the U20 (or whatever) would have been safely out of range.

Thus you see it mounted atop a Titan. There's nothing behind that cockpit but cameras, fuel tanks and maneuvering engines. Imagine the "stack" of a vehicle with the payload capacity of the STS on top of a booster... say, a Saturn V first stage.

Btw, Mark Wade pulls no punches in his opinion of Robert McNamara's decisions as Kennedy's SecDef. Scroll down the page (linked above) to the section just below the drawings of the X20 mounted on various boosters, and read the latter three of that group of five paragraphs before the next illustration.

The basic premise could have been: personnel in smaller resuable craft, cargo in unmanned vehicles.