Anything can be used as a tiebreaker whether it changes the outcome or not. Just because something can be used as a tiebreaker doesn't mean it changed the outcome.
This may be the first time I have ever seen a internally false tautology. So, in your world, "anything can be used as a tiebreaker" whether it breaks the tie . . . wait for it . . . or not?
Also, your world seems to contain the possibility that something that breaks a tie, actually doesn't change the outcome from being a tie?
You seem weirdly unable to simply admit that your claim, that there was some mathematical problem with using a scorecard tiebreaker, was wrong. And, if you want to go back, you will see that you raised that in defense of a claim that a scorecard playoff using the same holes as an actual playoff could favor certain players in a way that the actual playoff would not.
No matter which arbitrary detail about the scores you choose to announce as the tie-breaker, the total scores remain the same.
And this matters why? Any tie breaker is arbitrary if you are asserting that in relation to the choice of which tiebreaker is to be used. A scorecard playoff is not arbitrary in the sense that it isn't random or based on whim. And a scorecard playoff is not mathematically problematic as you first asserted but now want to change the subject from.
Longest drive is a skill. So, by your logic, if the tie breaker is declared in advance to be the longest drive on a 213 foot hole, then the tied player who most overshot that basket is the better player.
No. There is nothing about my arguments regarding a scorecard playoff not being the same as a coin flip that can be viewed as an endorsement of a long drive contest. You are reaching nearly epic levels of logical fallacy. Surely you aren't this dumb?
A scorecard playoff simply uses data from a round that isn't used to determine the initial socre. The true flaw in your reasoning is in your failure to understand that a scorecard playoff doesn't break a tie, it prevents a tie; what would otherwise be a tie is broken during the round.
If going for a tiebreaker is inconsistent with the strategy of going for the lowest score, it is not compatible with trying to win the game and no one will try for it. If going or the tiebreaker is consistent with going for the lowest score, it does nothing to tell us more about who played better than the score already tells us.
This is a silly "analysis." An announced scorecard playoff simply adds another strategy element when playing holes that are, or may be, part of the playoff, nothing more, nothing less. As stated above, it uses data not used to determine the initial score and that data can be described as "who played better on the sequence of holes beginning with hole x (where x is the hole that begins the scorecard playoff)." If you want to lay up on hole one instead of going for it on on your drive, approach or putt, that is up to you - you know the consequences.
I like a scorecard playoff. I like it primarily because it brings a tournament to an end and it is fair (i.e., it need not favor anyone in a way that they wouldn't be favored by playing the same holes that make up the scorecard playoff). It is evident that some do not like it, and that's okay with me. I have not tried, nor will I try, to convince you or anyone else, that you or they should like a scorecard playoff. However, your claims that it is somehow mathematically invalid (which is itself the attempted invocation of nonexistent scientific authority) are becoming more and more ridiculous the more your argue against it.
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