I think a better approach is to retain the existing rule (out-of-turn action stands if the current bet amount is zero or remains unchanged), but if the current bet amount is changed (by a bet or raise, regardless of amount), the out-of-turn player -- in turn -- may then call, re-raise, or fold -- but whatever amount was bet out-of-turn goes into the pot regardless of their decision (even if folding).the more I am thinking about it, the more I think this is actually a rule that punishes the out of turn action more harshly.
In our rulesets, the out of turn action is only binding if no player bets or raises in between the actual actor and the out of turn actor. So what this rule accomplishes the same thing as everyone checking in turn, action just immediately goes back to the person after the button and they have all options, instead of waiting for everyone to check in turn. However, this rule does not give the out of turn actor an "escape" if there is an intervening raise in turn, unlike our common rulesets in America.
So in short, I think rule hurts the out of turn actor more than our rules in two ways that I see.
1) The out of turn actor is denying himself position
2) The out of turn action no longer "benefits" from our provision that he may withdraw if someone makes a raise in turn
And I don't think one could argue the "skipped" players are at all damaged by missing their opportunity to check. They get to conceal their action longer because the player that made the mistake essentially forfeited his position.
I think I am actually warming to this as a good alternative.
This minor rule variation prevents the rule-breaker from getting an 'escape clause' but without artificially altering position in the hand, while the affected players still have the info of the premature act when deciding their own action.