>what part of getting an MBA filters for "possessing soft skills, being personable, ready to meet with clients or manage people and probably well-connected"?

An MBA is extremely team-driven. Classes are heavily discussion focused rather than having a lecturer simply teach a subject. There are lots of presentations and routine working with others.

I know all degrees have this to an extent but the MBA experience is exceptional in the level of collaboration needed. Because most of the people taking an MBA class have several years of real-world company experience, you end up learning heavily from the cohort as a whole rather than simple the "expert" professor.

I have a CS degree and an MBA and the difference in the amount of interpersonal effort between the two degrees is enormous.