In 2015 in AAA Schwarber hit .379/.419/.759 vs lefties. In AA, he hit .256/.373/.465 vs lefties. In 2014 in A+, he hit .265/.368/.531 vs lefties. In A, he hit .400/.464/.680 vs lefties. In A-, he hit .400/.500/.400 vs lefties. 2014 was 79 ABs. 2015 was 71 ABs. So, it's not the biggest sample size but he didn't just hit minor league lefties. He crushed them.
If people have the impression that he's a platoon type player I think that is horribly misguided. I literally think we're talking about the same thing Rizzo went through. Rizzo hit .172/.273/.345 in his first 29 ABs in 2011 vs LHP. In 2012 he hit .208/.243/.356 in 101 ABs. In 2013 he hit .189/.282/.342 in 190 ABs. It wasn't until 2014 where Rizzo broke out hitting .300/.421/.507 vs them followed by .294/.409/.472. and .261/.366/.466. Rizzo had 1913 PAs in the minors. Generally speaking about 25% of pitchers are lefties so that's something like 480 PAs against lefties in the minors plus another 200 or so in the majors before he figured out LHP. Schwarber has had some where between 200-250 since turning pro.
And that's the thing... the only way you get better is reps. I'm not a scout and there's no where near enough data to draw firm conclusions here but my best guess at what is going on here is you're talking about a player who was rapidly promoted and who got to the majors who has some issues vs lefties that he didn't have time to fix because he was so rapidly promoted. I mean it's entirely absurd that he made it to the majors only having 621 PAs in the minors. And major league pitchers being good at their jobs figured out a way to abuse an inexperienced rookie. He had a 8.2% bb rate and a 44.3% k rate vs LHP. There's no way that player is what Schwarber is going forward. He also boasted a .222 BABIP vs LHP which didn't help matters.
I think the belief of saying "sit him against lefties" is more or less a panacea to the idea of him not playing everyday due to his poor defense and his knee rehab. I think he's more than capable of doing it, I just don't think they want to push him that hard.
I think an interesting question could be would the Cubs ever roll out a 12 man hitting lineup and basically only give PA to the top 11 and have Szczur as emergency/9th inning guy? At 11, I think you can spread the PA around enough where your main guys all get 500+. You really don't have a need to PH that much in terms of offense so you're basically talking one or two PA for the pitcher potentially.
C
Contreras, Montero
IF
Rizzo, Bryant, Baez, Russell, Zobrist
OF
Soler, Schwarber, Almora, Heyward
Could be interesting if they did that and went after a fairly heavy bullpen of say specialists instead of a power arm. Keep Wood in there (who also functions as a 13th position player), add Logan, move Montgomery to the rotation and give a shot to a young guy or two who earns it out of ST.
5 starters
Rondon/Edwards/Strop - back of the bullpen
Grimm/Logan/Wood/ - situational guys
Johnson/Zastzyny/Others - mop up
The Cubs had a ton of innings of "low leverage" so I don't really see the need for this massive bullpen in terms of value.