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.