It's an interesting topic, and a broad one. You are looking at it from the perspective of both the pitcher and the batter, not to mention the managers who have to think these things through.
A batter who isn't a defensive whiz needs to survive through his bat, and that means this: murderize the pitches that come from the opposite hand, and be at least playable when the pitches come from the same hand. Wallner's career splits are extreme but one can view his 2024 as representing progress of a sort, with an OPS of .611 against lefties. That's not good, and at age 27 it's not clear how much additional growth he's capable of, but even a little further improvement against LHP will make him "not unplayable" when the average lefty takes the mound. That's all he needs. A walk instead of a meek putout, against a lefty during a rally, makes all the difference, for example. (Wallner is also know for HBP but I don't really recommend this as a conscious strategy.)
Larnach is in a less favorable position - his 2024 didn't give evidence to feed him more PA versus lefties. It's a big assumption that more and more chances will improve matters - it might, or it might lead simply to losses.
On the other side of the coin, nothing is more maddening to me than to bring in a lefty, say with two outs and men on base, to face the other team's LHB, and for that pitcher (*cough*Thielbar*cough*) to then fart around trying to lure swings at pitches out of the strike zone, eventually walk the batter, and then have to face the righty because league rules no longer allow the LOOGY. YOU HAD ONE JOB, lefty, and that's to attack the left-handed batter. If he beats you when you gave him your best stuff, so be it - you're in this to compete, right, so sometimes he gets you, more often you get him.
It would be interesting to extract statistics of how pitchers do when facing alternating handedness. I have no way to develop that data myself.