Yeah I dont think I like the idea of troubleshooters at all. It sounds very min/max. I like stat and skill dependency because I want MAD characters. The troubleshooter method sounds like you can have your cake and eat it too, but that totally depends on the player playing up the dumps. Im seeing red flags already with players I know.I kinda don't mind it if it means balancing things that are sort-of equally important. For example, one stat determining accuracy, another power (damage), and a third endurance, and needing to balance these against one another.
There are two problem with this, though. One is that it's only interesting as long as the stats are reasonably balanced against one another. In D&D, they're generally not. Accuracy and power are generally the same stat, which skews the balance. The other is that if you add stats outside the prime ones, they tend to become dump stats by necessity. So a fighter will have great Strength or Dexterity, good Con, and likely mediocre stats otherwise. It really isn't possible to be good at both social stuff and a competent fighter – no popular jocks or himbos here.
That's why I like the way the Troubleshooters does it: there are no interdependencies between skills. You want to be the world's best lockpick while also being loud and clumsy? Just get yourself a good Prestidigitation skill and don't worry about the Agility or Stealth skills. It also neatly bypasses the discussion about what skills should be based on what stats. Should Intimidation be Strength, Charisma, or either? None! That way, things are open for both the Gentle Giant (strong but non-scary), the Thug (strong and scary), the Creep (verbal and scary), and the Bard (verbal and non-scary).
I would prefer to leave skills as is (well actually greatly expand the skill system but that's another thread) and look more at damage, accuracy, perception, and initiative. I'd prefer to remove stat dependency from those things. I really like the idea up thread about having a primary stat, a secondary stat, and a tertiary stat based on sub-class. I'd lvoe to go even beyond that, but due to 5E design thats just not in the cards. Essentially, I want to get away from every fighter has x,y,z array and every wizard has a,b,c array like we have in most modern games now.