LORE QUESTION!

I know we've gone over this a few times, but I wanted to discuss the proposed roles of the Primarchs and Legions in a hypothetical, functioning Imperium. I don't think I've ever read a satisfying answer for certain Legions. Here's what I've got:

>DA
No fucking idea.
>EC
Arts, humanities, promotion of culture
>IW
Architecture, civil planning
>WS
Exploration? Expansion?
>SW
Execution force
>IF
All things Terra
>NL
Judiciary and correction
>BA
No fucking idea, maybe an "official face" of the Imperium?
>IH
Technology, ambassadors to Mars
>WE
No fucking idea, maybe a return to gladiators? Bread and circuses?
>UM
General administration
>DG
Health department? kek
>TS
Records, libraries, education
>LW
Law enforcement
>WB
Propaganda, information logistics
>SM
Craftsmen, trades, possibly family services
>RG
No fucking idea
>AL
Stasi, creating controlled opposition conflicts

A few are completely baffling. Then again, it's not like all of this was hammered out by one dedicated author. Thoughts?

>TQ
Constitutional Carry