…, credits earned by a commander during an activity would have absolutely no effect on the BGS.
…
Firstly, let's just agree on this. A faction losing money, in isolation from anything else, would not be of benefit. …
I agree with you, that influence and reputation should be based on the activity or action.
But - credits in this game are used as a way to indicate how important activities and commodities for a faction are. If a CMDR makes a profit or earns a lot of money, then that CMDR is doing something the faction wants to be done and while the faction spends money on that that faction gains something they value more than the credits - commodities, jobs that got finished, problems solved.
In Elite credits are used as a way to measure how important, needed and useful something is.*
The whole problem of trading could be fixed by making the price match the demand more closely and selling goods that are not needed should result in no profit at all. In that case selling goods at a loss should have no impact on the BGS - way to easy to exploit and since buying stuff at a loss doesn't make sense and is only a result of a rather rudimentary economy system it can be ignored for the BGS.
Not trying to get into details and concentrating more on the big picture:
Credit value of activities could be seen as a proxy for transactions. The different credit rewards for activities functioning as a way to balance the importance/influence of those activities.
Adding everything up would then be a nice simple way to get an easy to understand system.
The main problem with this approach is, that the amount of credits earned are constantly changed - players demand more credits for various out of game reasons.
This makes a transactional system, while more complicated, a better choice as the credit rewards can be adjusted independently from the effect on the BGS.
But overall I don't think the discussion should be about transaction vs. value, it should be about what the BGS should be and how it can be turned into a system that works for the majority of players.
*) btw: that's why credit farming "exploits" are so problematic