Mike,
Ash stated that the folding players acted quickly...
Not sure why you selectively read the OP. Verbatim it reads:
"player A is thinking, players B and C fold, player D also folds supposing it is over, and then player A says he is still there. Neither the dealer nor the other players saw A had still his cards".
Nobody including the dealer saw Player A's cards which were "hidden behind his chips". While B and C may have "folded quickly" they did so in turn, meaning that, unlike A, they were following the action. I've played poker many years and can't recall a situation where 3
attentive players discard so quickly that a 4th player can't follow their action and speak up.
also, why would Player D fold his hand before the dealer awarded him the pot?
While that isn't good form on D's part, 1) people toss their cards forward "in exchange" for the pot all the time and 2) nobody thought A had any cards, he had them hidden and made no effort to speak up.
I have not looked at any "new" rule changes from the most recent summit but I have a feeling there will be at least one controversial addition.
No doubt you'll find something in 2017 to disagree with, but Rules 2, 25-C and 43-B have been affirmed for three Summits now... they were all adopted in 2013 (Rules 2, 24-C and 38-B back then:
http://www.pokertda.com/wp-content/uploads/2013/08/Poker_TDA_Rules_2013_Version_1.1_Final_handout_PDF_redlines_from_2011_Rules.pdf)
There are dealer procedures that must be followed and that seems to be where most of these problems originate.
Each situation is different... in this case nobody at the table saw A's hidden cards (a violation), and A either didn't follow the action or if he did he decided not to defend his right to act, both also Rule 2 violations. The primary problem here isn't with the dealer, it's with Player A.
Let's look at what went wrong. #1) Player A is skipped....
Before this, what went wrong was that A hid his cards and unlike B, C, and D didn't follow the action or defend his right to act.
#2) The dealer also fails to notice Player A was skipped...
Why would the dealer notice that? Nobody saw A's cards according to the OP.
#3) Player A fails to stop the action before Player D folds...
So now there are 3 players folding to his left... typically that's substantial action. The twist in this situation is that the last "folder" is also the last player at the table... so does that constitute SA? That's what the TD has to decide here.
There were multiple mistakes made by everyone at the table. However, for you to say that in many venues Player A should have a dead hand is ridiculous. Barring an obvious intent to hide his cards under the table, or some other devious tactic, Player A is the only player with cards and killing his hand is criminal.
Player A has committed "crimes" to use your term against at least 4 TDA Rules. It doesn't matter what A's intent is here... only what his actions are: not keeping his live hand visible at all times, not following the action, not defending his right to act, and ultimately allowing SA to occur to his left after being skipped.
What do you do with the pot if you decide to kill Player A's hand? 
If the decision is to kill A's hand, then D would be the winner. He's the guy who knocked B and C out, and A knocked himself out by not speaking up and allowing SA to occur to his left. See Rule 43-B. "... including ruling a dead hand as the TD sees fit under the circumstances". Believe me, there's a large contingent of TDs who would like to see the hand ruled dead
everytime SA occurs to the left of a skipped player, assuming that player had reasonable time to act.
