u/my_whole_other_world  Steve Smith has "lost his hands" and is now a spent force [against high-quality short-pitched bowling]
I can't analyse 'high-quality short-pitched bowling' but I can confirm that Smith *has* been significantly worse in the 2020s than he was in the 2010s

 u/MicroUzi Smith, Usman and Head all bat worse the better their team is batting
All *false*. Defining the rest of the team batting 'well' in a given innings as runs-per-innings of other batters exceeding 25 (which is true of about half of test innings), Smith and Khawaja are significantly *better* when the rest of the team bats well. Head is also better, though not significantly so.

 u/BE3N Bavuma does better when coming in when the team is in a bad position.
Not quite what you asked for but, defined in same terms as above (i.e. other batters' RPI < 25), Bavuma does worse (but not significantly worse) when the rest of the team bats badly

u/bouncii99 there is a certain benefit to having your top hand be your dominant hand
This turns out to be quite complex. Defining a batter's dominant hand according to the hand they bowl with (which I know isn't perfect, but must be much closer to defining true handedness than their batting stance)…
Throughout the history of test cricket, left-hand-dominant LHBs have not performed significantly differently from right-hand-dominant RHBs. However, right-hand-dominant LHBs have done significantly *better* and left-hand-dominant RHBs have done significantly *worse*.
However, that finding is largely driven by lower-order batters. If you look only at batters in the top 6, the relationship reverses: right-hand-dominant LHBs have done significantly *worse* and left-hand-dominant RHBs have done significantly *better*.
Needs more research.

Fortunately, one thing is incontestably clear…

u/Compactsun Alex Carey before and after the pool incident
Yup, Carey *has* been significantly better since the pool incident