I figured 'it' out after one year of D'Antoni but not quite the same 'it' as yours or Sunsfan's. Its far from clear to me that Nash's style encourages FO's and coaches to shun defense and make bad personnel decisions. We have had a weak D culture in Phoenix almost from the very beginning. I want to dump Gentry because he didn't recognize it last year when the second unit was having success due to defense - which was an opportunity to start changing the culture.
Yes, Nash's individual defense is poor but a good defensive team could cover for him enough so his net effect on games would be positive - heck, its strikingly positive now with this team.
Anyway, you need to break Nash's style down to two components - pushing the tempo and half court game.
No one will ever convince me that a fast tempo is bad basketball - the Auerbach Celtics and to a lesser extent the Showtime Lakers played very up tempo and were both terrific defensive teams. Many time champions, too, in case you're not aware of history.
Nash's freelance style in the half court is more problematic and, of course, the problem with it shows up when he's not on the floor. Its mainly a coaching problem and the first hurdle for the coaches is to recognize it and face it head on because they have virtually no chance of finding a backup that can successfully play Nash's style.
Its really not an insurmountable task for the players to learn a goodly chunk of a normal NBA playbook plus what is required for Nash to operate - Jackson's teams have to learn the triangle offense which is reputedly much more complex than typical NBA offenses. They seem to manage, somehow.
Of course they have to practice the plays the backup PG will run, which is probably a more difficult task. Its not entirely wasted time because they need to practice defending against those plays regularly anyway. The biggest hurdle many coaches would face would be delegating the responsibility for the backup offense to an assistant so there's someone who worries about it full time - and has the authority to do his job properly.
If the team is deep enough you could 'two-platoon' the way the Suns did the last half of the season last year. Personally I like this approach but I realize that a couple of untimely injuries could send your carefully laid plans down the crapper. Or a FO that was more concerned about making good deals than with giving the coach what he needs.
I'm certainly not advocating keeping the Nash style alive at this point. I want a new, better coach and at this juncture in Nash's career I think the coach should determine the style. If he wants to keep Nash and Nash wants to play for him, let them hash out how to transition to post-Nash era.