I had the itch to play this a few weeks ago but just really couldn't push through it. I want to play a game where I control most of the grand strategy, but not really any of the construction and setup. I just use what they have, being able to play both on the global planning/movement side (setting up fronts, full invasion plans, etc.) as well as individual battles. Sort of a la WarGame but a more in depth global campaign mode.
With HOI3, you could turn on the AI for any of the functions you don't want to handle personally - then that part will be as stupid as the other countries, so you'll probably have a more challenging game
I never use the AI for research or production or trade because those are the fun parts to me, but I tried out the "semi AI control of armies" and it wasn't completely hopeless and DEFINITELY cut way way down on micromanagement if you could stand the inefficiency.
I don't remember which features of it were added in patches or in the various expansions, I know you could designate "axis of advance" in the last one ("Finest Hour"), which definitely helped keep the invasion of France from turning into the war of attrition that used to happen when you left it all to the AI. And you can switch on/off AI control of subtrees of the Order of Battle, so if you want to just control say a couple of key armored corps and let the AI handle the rest, I know a few players were playing their games that way...
It's still a huge nightmare to jump right into playing a global Major Power, as there's stuff happening all over the world and 20 billion details to try to pay attention to. I definitely recommend building up to it through the scenarios (Spanish civil war, Brazil/Argentina) and getting used to parts of the system through playing minor countries first - Poland with a 1939 start, then some 1936 starts to see how long you can last, Nationalist China gets into a fight pretty early in the game, and you can ignore (heh can't really afford) air and naval forces any time soon. An Allied regional power like Canada or Australia, and focus on supporting the Allied cause with naval or air power, then maybe something like Italy, which needs all 3 air/ground/naval but is small enough in size/scope to be manageable.