Basically every argument you're making is one that speaks to its lack of a thing.
1) #s in the playoffs are small samples and inherently swingier, making real conclusions and observations on them suspect at best
2) suggesting it's there for some and comes and goes for others points to its unreliability. If only a very small handful of players can demonstrate consistency and everyone else is subject to wild variance then it's hard to suggest that the variance isn't the norm and the few nodes of consistency aren't just the fact that sometimes you flip a coin and it gives you 10 heads in a row, especially if the coin is already slightly weighted towards heads (in this analogy the weighting is the possession of overall high inherent skill). If it were a true repeatable skill then players would be consistently good or bad at it on the whole
3) mushy/vague and anecdotal claims in lieu of hard evidence speak more to our ability to see patterns where none exist rather than real observation. Of course we remember the times that stand out or conform to expectation because we don't remember everything and those things are by nature more memorable.
David Ortiz:
.286/.380/.552/.931 career slash line (avg/obp/slg/ops) (10,091 career Plate Appearances)
.296/.411/.531/943 (3014 PAs) with RISP
.276/.417/.534/.870 (1299 PAs) RISP w/2 outs
.256/.371/.499/.870 (1451 PAs) in "late and close"* situations
.289/.404/.543/.947 career post-season (369 PAs)
Jeter offers similar #s. I don't want to type everything out but it's .817 career OPS, .810 with RISP (3112 PA), .816 RISP/2 outs (1380 PA), .776 Late & Close (1725 PA), .838 post-season (in 734 PAs vs over 12,600 regular season career)
*Baseball-Reference defines "late & close" as any situation in the 7th inning or later where a) the game is tied, b) the batting team is leading by one run, or c) the batting team is has the tying run on deck (including situations with runners on base to account for larger deficits)
I can't find post-season splits likely because most places won't carry them in easily filed locations since they're going to be so limited as to be almost valueless (if you consider that those RISP and late/close splits are like 13-30% of a player's career plate appearances, then you're talking <100 PAs for all but the longest-running playoff qualifiers for any situational split.
The crux of this is that yeah, those two have slightly better post season batting #s than their regular season numbers. But they also may tend to have slightly worse regular season "clutch" performance #s than their baseline regular season #s. If clutchness and rising to the occasion was a consistent and repeatable skill, they should show growth and improvement in most or many important situations but they don't. The only one they do is the one that also has the least amount of evidence and is therefor subject to the greatest amount of variation (a WS run might see 60-70 plate appearances, enough to make a big dent if he struggled. For instance with Jeter, in the Yankees' WS loss to Arizona he notched 62 plate appearances for the entire playoffs and hit .193, largely buoyed by throttling the A's in the ALDS)
Suggesting that clutch hitting doesn't exist as a repeatable skill also doesn't mean that nobody will ever show a hitting profile that suggests them 'rising to the occasion' or whatever. Outliers are a thing that happens in statistical analysis. Good players are going to have moments of doing well in important situations and it's going to give them the reputation of being better in those spots. The issue is that if not enough people are better in those spots, and people in general are not consistently and regularly better or worse in a repeatable fashion, it means that the observed ebbs and flows are
For instance, I may not have situational splits, but a quick bit of napkin math on Jeter's postseason game log shows he went hitless in 9 of 38 career World Series games and had just 1 hit in 19 more. So in 28 of 38 career games in the world series he batted (likely) .250 or worse if we figure an average of 4 plate appearances per game. And then this is offset by those other 10 games where he would go 2/4, 3/5, 4/4 or whatever and push the average up significantly.
And just for a bit of added info, in those 19 1-hit games he had 2 HR and 3 RBIs (obviously only 1 of which was an RBI from a base hit and not him just hitting a solo HR and getting credit for himself). So those times where he only had the one hit it isn't like he was making the most of it (across the 28 1-or-0 hit games he had 11 runs scored. if we take off 2 for the HRs that means he was cashed in by other Yankee hitters 9 times in those 28 games or like 110ish plate appearances. Good for him but the Yankees generally had thunderous offenses and runs scored is not so much indicative of a player's skill as it is the skills of those around him)
basically I'm not saying that clutch performances don't exist nor that nobody's ever seen somebody do something big in a big moment. What does appear to be true is that the ability to rise to the occasion and be clutch when it matters on an ongoing and repeatable basis is more than likely not real. Good players are going to have good stretches which includes good output in big moments sometimes. But it rarely happens with the consistency and predictability to suggest that it's a skill that can be captured and declared repeatable.
I don't have time right now to go back and find the previous post (I was supposed to be backing up the files on my computer because I'm starting to get some curious behavior from its hard drive that's making me give it side-eye but instead I've been down the rabbit hole on this issue and now it's 3pm and I have to go make dinner in like an hour and a bit) but I'm fairly certain I previously linked to a bunch of studies that were conducted on the concept of clutch performance and found that there's not enough evidence to draw a strong conclusion in favor of its existence.
EDIT: One quick link that went in on clutch hitting (using regular season performance):
Is clutch hitting an identifiable and replicable skill?
www.baseballprospectus.com
It's a ton of math, much of which can be difficult to decipher if you're not familiar with some mildly obscure metrics on run creation and win probability, but the gist of it is that using a variety of measures to examine clutchness, they found some curiously noisy results including what I wanted to highlight:
based on the criteria set, David Ortiz was in the top 5% most clutch players in MLB twice (2005 and 2006) and in the bottom 5% 3 times (2007, 2011, 2013). Tony Gwynn (4 top performances, 2 bottom), Joe Morgan (3 top, 2 bottom), Frank Robinson (2 top, 3 bottom), Pete Rose (3 top, 2 bottom) and Larry Walker (2 top, 2 bottom) were also among a group of players that appeared at both the very top and very bottom of their leaderboards multiple times each across their careers. And in most cases the appearances do not line up in a way to plot a trajectory (starting good and getting worse or starting bad and getting better) and instead are simply all over the place at random. The conclusion of their research is that players can be clutch, but they are rarely if ever repeatably clutch (or unclutch) over the course of their whole careers.
