The argument that pitchers choke based on postseason numbers is where the conjecture is.
Is it possible? Sure. Is it the only possible reason? Absolutely not.
When a pitcher has lots of postseason data, it has to be spread out over multiple seasons. In Kershaw’s case, it’s 13 years. Most pitchers just aren’t the same pitcher over that stretch. Really, rather than being one big sample that can be summed up solely with ERA, it’s a series of small samples being stuck together and called a big sample. I doubt 2008 Kershaw had all that much in common with 2020 Kershaw beyond the number on the uniform.
And pitchers are on average more affected by longer seasons than position players. And are susceptible to a wider variety of injuries. Was Kershaw healthy and pain free across 13 post seasons? Did his various workloads affect him differently each year?
Really does this example prove Kershaw simply couldn’t handle the pressure? Or that he didn’t handle physical pain as well as, say, Schilling did?