Three player's remain; dealer burns and turns before last to act player calls. In this scenario, the "skipped" player is skipped by the dealer. You're not going to kill his hand...are you?
No, because betting is not complete, see RRoP.
I mention this because it would offer no support to killing a hand after substantial action, and certainly no possibility of SA + 1...
Betting is not complete in your first scenario above. However, if SA or SA+1 had occurred prior to dealing the next card, betting would have been complete, and there is virtually 100% support expressed at Summit VI for killing the hand if SA has occurred PLUS the dealer deals the next card. The reason that wasn't written into the TDA 2013 Rules is that it might leave the impression that is the only situation in which a skipped hand is dead if there is SAOOT, and as previously discussed in this thread, there are two camps, one of which will kill the hand
on the current betting round if SA occurs... and permutations that will kill it on the current round if SA plus some additional action occurs.
The perfect scenario, (to get my point across) is; Multiple player's: First to act bets, next player calls, next player is skipped by last to act and the dealer burns and turns. In this case, only one player has acted after the skipped player. Do you feel the skipped player's hand should be killed? Or does the premature board get re-dealt?
IMO the board is re-dealt b/c betting is not complete on the prior round. So in this case "dealer does not count as action".
I believe my examples point out the need for dealers to be recognized, as one of the persons included whenever we consider substantial action.
On the contrary, IMO your examples point out the need for the dealer
not to be recognized as an acting player for SA (i.e. the dealer is not the "second player with chips" or the 3rd checker/folder"). What everyone agrees with is that if SAOOT occurs, those bets are binding. THEN if the dealer deals the next card, the skipped hand is dead. But in that situation the dealer is not counted as one of the actors to establish SA, he is in addition to SA.
This is a separate issue from whether (and if so when), a skipped hand is killed on the current round.
Back to dealing the next card counting as part of SA: personally I think including "dealer is part of SA" is just an unnecessary complication. RRoP clearly states in at least two places that "the card will be re-dealt if betting has not been completed". It's just easier to leave it there.