Study the chart and trust in it. Don't worry too much about "why." If it's an accurate chart, as it probably is, it is derived from millions of simulations of that hand. It needs to be followed religiously.
I realize you were just giving an example with your post title, but it's a bad example. Why would you EVER stand with two aces? You CAN'T hurt yourself one single bit by hitting... but you certainly MIGHT improve, with an 8 or a 9, for example. You can't make your hand any worse with a hit.
And yes, you're correct... you know you're supposed to split those aces. But there are other examples where you must hit vs stand. I've seen player's stand when hitting on a soft total will NOT hurt them at all, but MIGHT help them. In those situations, ALWAYS hit.
With an Ace and a 4, aren't you supposed to double on that, against a dealer's 5? So your additional details question is irrelevant here too.
For all practical purposes, if you have 15 (for example) it doesn't matter HOW that 15 is arrived at, or how many cards you have. Make the same play as you would for any other combination of 15.
Again, study the chart. Learn it inside and out, forward and backward, so that you instantly know the proper decision to make on every hand.
I own almost 40 books on blackjack and I've been playing the game for almost 40 years.