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.

Only for asteroids we can predict collisions with well in advance.

The Asteroid Redirect mission that was supposed to happen a few years ago was cancelled due to lack of funding. DART is the replacement mission that was able to get funded.

Yes that is probably how we will do this next. But fat ion engine and some solar panels or maybe nuclear power station