It's a good summary of the probabilities, but amounts to preaching to the choir.
It won't convince the fan who believes
Ground ball: good, a chance anyway.
Fly ball: good, a chance anyway.
Whiff: bad, no chance
The problem is when you conflate results with what the batter was trying to accomplish. The latter is much more complex to analyze. The table of probabilities concerns itself with the outcomes, and you might say that it suffers from the weakness of not considering the alternative outcomes that could have happened from the same approach at the plate. But the Whiff Bad point of view is even worse because for strikeouts it only considers the outcome while for groundballs especially it subtly mixes in the view that the ball might sneak past the infielder anyway, ignoring that those outcomes are already included in a batters hit total or the records kept on errors. This is exemplified when excusing a mediocre batter, "sure, he hits only .200, but he hardly ever strikes out."
Compare the above list of 3 outcomes, versus the paragraph I just wrote to delve a little into it, and it's not surprising that the former has a lot of staying power. Baseball's just a game after all, not an exercise in Bayesian probabilities for most people.
The batter who strikes out when trying to launch a three-run homer to win the game doesn't get credit for that potential homer in that particular at bat. Which is fine, but even those homers that a decent power hitter gets are devalued by the anti-strikeout fan with a mention of the Ks that go with it. Decent singles hitters aren't held to that same standard - "oh, sure, but he grounds out too much" does not factor into many discussions.
The batter who strikes out by looking at a close pitch on a 3-2 count may have judged that his best chance for a good outcome was to lay off of what looks like an unhittable pitch down and away. The cases where he guesses right are simply chalked up on the scoresheet as a walk, which many fans will immediately denigrate as not as good as a single, ignoring the situation that on this pitch a base hit was unlikely.
The batter who grounds out may have done so because he tried to pull a pitch that was farther outside than he expected, meekly grounding out to a middle infielder. The fan who hates strikeouts will cheer that at least the batter gave himself a chance, even after the outcome is registered by the first-base umpire.
This doesn't even touch on the even more important (and complex) question of what happened earlier in the count. That backward K may have occurred because it was set up on the previous pitch when the batter swung through a meatball pitch that might have gone for extra bases.
It's very hard to construct an apples-to-apples argument because the focus on the outcome is only part of the story, and the typical fan understands this when it comes to grounders and flyballs but gives no benefit of the doubt to the result that's a K. Partial analyses are dangerous because they are true but misleading.
Of course all analyses are partial, so one has to pick where they think stopping is least dangerous. As I implied, the probability tables in the referenced article are also a partial analysis. The whiffs-are-bad fans simply choose a different stopping point than others. No one has a complete analysis.