The thing is though - if Phil was coach, would Nash be healthy enough to get down enough Triangle reps with the 1st unit in order for the team (as well as defensive situations) to capitalise (at a maximum state), on it's 1-season championship window.
Lakers would be dealing with a double-edged sword either way.
I don't think Nash would have problems learning the triangle, he is a veteran and Suns played against Lakers so often, he should already be familiar with it. How effective he would be personally in the triangle is a different question. Kobe and Pau already know the triangle and Pau is a good passer, so Phil's offense would suit this team much better. Whenever Kobe would sit Bynum and Pau looked good together. From what I've heard and read from former players, triangle is not that hard to pick up. Steve Kerr said Nash would pick it up in 30 seconds.
D'Antoni's offense doesn't work because 1) the squad is too old and slow to run and keep up the tempo every night. 2) the Lakers have no shooters to spread the floor. 3) D'Antoni's offense doesn't work with two big men clogging the lane (Shaq/Amare or Tyson/Amare or Amare/Melo on the block). D'Antoni didn't use Amare in the post when he had him with the Suns. 4) Nash is old and who knows how true the myth of Phoenix medical staff is. Either way you can't expect him to play 30 minutes a game anymore. And you don't want Duhon running D'Antoni's system. Phil could dig up Fisher from his grave and still have him run the triangle effectively.
Lakers are fukked defensively either way. Kobe and Nash in the back court, Artest getting slower, that bench . But D'Antoni had to bring in Woodson in his 4th year with the Knicks to improve the defense (what kind of fukkery is that?). So don't expect any fixes from D'Antoni especially if he tries that 7 second or less bullshyt. Phil at least knows and likes to use centers, especially defensively.
But I still expect Mitch to go to work and get them what they need.