The website Slate had a series suggesting changes to the consituttions. One was making Attorney General an elected position, to better be the people's lawyer and keep the President in check.
http://hive.slate.com/hive/how-can-we-fix-constitution/article/picking-the-peoples-lawyerThis plan has some disadvantages, as it forces Attorney Generals to be able to wage national campaigns. And it creates a launching pad for the White House that is limited to lawyers.
Cabinet members seem to be like being able to serve partial terms, something that isn't as appropriate in elected office. There's the potential for conflict, especially with overlapping offices held by different parties (A Republican Secretary of State, and a Democratic Secretary of Defense, A Republican Secretary of Treasury and a Democratic Secretary of Commerce.) It's also a bit restrictive to keep the offices only for those who wage national campaigns for it. Right now, the same person might be considered for multiple cabinet positions.
I did wonder who would have won Attorney General elections, and how that would have changed things.
Geraldine Ferraro might have been elected to the office in 1986, as a former prosecutor with national name recognition. Or the same things that doomed her senate campaigns could have doomed this. We likely would have had a milestone of the first woman to hold national office by now.
If John Kerry had run and won in 1998 (he had the resume and it was a cycle in which Democrats were competitive) he probably would have been Gore's running mate.
2002 would almost certainly have seen the election of Rudy Giuliani to the office.
2006, assuming similar political circumstances, would have been a very Democratic year. I could easily imagine a tough primary fight between Eliot Spitzer and John Edwards.
Charlie Crist might have stayed with the Republican party, if this was an office he could have run for in 2010. Or he might have lost to a tea party affiliated challenger (not sure who.)
2014 would likely have seen the reelection of the Republican incumbent.