It would help, even with a selfish donkey reading every magazine without sharing.
Reason being, the OP described a situation with at least 3 players.
If 2 of them are looting, the guy who holds mags for the OP is going to get the boosted chance, with which they'll be able to share relevant magazines to the OP who isnt looting.
In my first coop save, I was looting primarily, and my skills let me craft T5 Steel Spear by day 5, while my friend managed to only get to T1 Double Barrel, despite me feeding him any Shotgun drops i happened to come across.
In the second save, we did the split looting, but all that did was cause us both to still be in pipe weapons by the time the horde rolled in.
By making it so the party as a whole gets boosted odds for magazines relevant to each party member, even having just 1 player sharing can make a difference.
Back in A20, lootstage was a party deal. So it didnt matter who opened a crate. But it does now, because the probability boosts are player specific.
I am more likely to get a medical magazine in a medical pile than my friend is, so anytime he opens one we have effectively lost a medical magazine. Thats not a good system.