Let's be very generous to this card an look at it from the point of view of early Netrunner: Jinteki is even poorer than the other corps, and Account Siphon is everywhere. If you're ever going to over-advance this card, it's going to be the first one you draw, early on when there's not much ice rezzed yet, and you can pretend it might be a Junebug or Fetal. Even then, you're risking a big setback if it's stolen after you spent two clicks and two credits on it. Purely for its economic drip/boost, that's arguably not worth it.
What an over-advanced Braintrust does give you, however, is the ability to rez a select few pieces of ice despite having been siphoned down to zero credits; for early Jinteki, the most relevant ones are Chum, Ice Wall, Hunter and Snowflake.
I don't know how extensively early Jinteki players experimented with using Braintrust along those lines, but it's likely over-advancing it simply proved too risky and unreliable for a viable strategy. Regardless, I'm fairly certain that this was the design intent behind it.
