Long term, an asteroid-to-orbit mission has several benefits:
- geopolitical value
- asteroid defense value
- economic value
- scientific value
Capture of an asteroid has several geopolitical considerations that give it value, ones which don't require manned missions by anyone.
The proven ability to move asteroids into orbit, especially lunar-coorbit (LaGrange points) or Lunar orbit, would establish definitively a level of fine control over asteroid movement. That level of fine control is a requisite for use of asteroids as weapons of mass destruction, and is directly on par with orbital insertion.
This is undoubtedly a part of the considerations - such a practical capability is bidirectional - if you can put one into stable orbit, you can also crash it, and also send it away from Earth. In other words, by proving you can make a successful insertion, you prove you can prevent one, as well.
The commercial applications, much as with the Apollo program, are a justification, but are probably not the root for the program. (Apollo established that the US could in fact deliver a missile payload anywhere desired within cislunar space.) The mining value of a nickel-iron asteroid as base metal is not worth the effort - it would cost more to recover the metal than the metal is worth. One that has significant other metals would be financially valuable, but the programmatic costs and landing costs may not be viable long term. Planetary Resources thinks they can manage it and make money - but if they had secure numbers, we'd see backers lining up to privately fund it. The risk is too high. (Further, the geopolitical aspects make it impractical to pull it off without it looking like a threat.)
The scientific value of an asteroid to orbit is immense - on par with putting men on the moon, but only slightly so. In addition to the mission itself and its science value as a near-system trans-lunar mission, there is the benefit of it being a platform for a much more radiation-proofed space platform, which would enable truly long-term science missions in microgravity.
The combination makes the asteroid to orbit overall a higher priority for politicians than the pure science of further lunar missions or the science adventure of Mars.