It's all about how much energy we can transfer to the asteroid, and a spacecraft moving through space at 6.1km/s is carrying far more kinetic energy in its own velocity than it could ever carry in fuel. Crashing the spacecraft into the asteroid and transferring all of its own kinetic energy into it is way more efficient and economical than trying to land it, then use a thruster to steer it away.

Keep in mind we don't really need to "steer" it, we only need to nudge it in a general direction that we know will affect its orbit enough to miss Earth.

Additionally, any thruster we do use for such an application would likely have to be an ion engine of some sort, because otherwise the specific impulse of normal chemical rockets would be far too low. We'd have to send a ton of fuel to make any noticeable change to its orbit. However, ion engines provide barely any thrust and would take years, if not decades, to push the asteroid by any noticeable amount - which also means we'd need to notice years or decades in advance. Transferring all that energy in a single instant with a kinetic impact event is much better in that regard.

Every answer telling you some supposed reason about why this is infeasible or ineffective is wrong. NASA and related, credible parties have conducted studies and generally conclude that a nuclear device is one of the most effective strategies we have of asteroid avoidance. The catch is that it would not be used in the manner you describe to "disintegrate" an asteroid - rather, it would most likely be detonated in a surface standoff detonation and use the vaporized surface as ejecta to propel the asteroid in the opposite direction.

https://web.archive.org/web/20160303220543/http://www.nasa.gov/pdf/171331main_NEO_report_march07.pdf

In the case of a large and/or imminent threat, this would likely be one of our only options. No other feasible strategy, whether kinetic impactor or gravity tractor, is capable of transferring so much energy to an asteroid in such a short amount of time. DART and the gravity tractor approach are both similarly mature technologies, but they require either for us to see the threat years in advance or for the threat to be very small - possibly both. A nuclear device is capable of redirecting a much larger asteroid with a much shorter notice.

There are technical challenges to address, yes, but relatively minor ones especially given the level of spaceflight technology we've already had for decades.

The obstacles right now are geopolitical, not technical. The Outer Space Treaty bans the use of nuclear weapons in space. That means we can't even test it. The DART II mission that /u/ItsMyImPulse mentioned would certainly be interesting, though - a dry run to confirm our technical ability to pull off a mission like this would do a lot for our preparedness in case we ever do need to actually do it, without violating the treaty.

No you wouldn't. The most realistic option for a nuclear avoidance strategy is to use a surface standoff detonation some tens or hundreds of meters above the surface.