Ok, I'd like to do exactly what you say to do. I'm looking at the Astros lineup and stats last year. Let's take one of those positions you mention - Palka and the DH slot. Last year, the Astros primary DH was Evan Gattis, and they also rotated a n umber of people there. Evan Gattis put up 0.4 rWAR, a .736 OPS, and was paid just under $7 million for that. Marwin Gonzalez put up a .733 OPS for them and 2.5 WAR because he got a lot of at bats filling in for the injured Correa. Jake Marisnick put up 1.7 WAR and a .674 OPS because he was their utility OF and defensive replacement.
These are guys like Palka and Leury. They're not great players on their own, but they have a couple benefits - they fill a role, they're already there, and they are cheap. Some of these positions we need to upgrade over - I'm about done with Leury for example as I don't think he can stay healthy, but there's a fair question here. Pederson will be paid like $5 million this year and it will take trading some player of decent talent to get him. Yes, he's an upgrade over Jay in CF, but that upgrade isn't free. You're spending more money and giving up a player who the Dodgers want somewhere, and you're doing it for a moderate upgrade over guys that the Sox already have come up with.
So is it true the Astros have no one like Palka? I very much disagree, their team put up a .749 OPS out of the DH spot last year and we outhit that thanks to Palka. Is Pederson on paper an upgrade over Palka in the OF? Yes. Is he worth the cost to the White Sox? Well as you said, only if you think this team is going to be 28 wins better than last year and you need Pederson to push it to 30.