A "going concern" is a business that is operating and making a profit. A "going concern warning" is a term of art that implies that a company's situation (usually fiscal) is such that it may need to stop operating. In other, smaller, contexts disasters like a loss of key staff trigger that kind of warning.
Bottom line, as you say: "Going concern" = "viable business"
For more about the history of the field of accounting: https://en.wikipedia.org/wiki/Luca_Pacioli
Source: Am CPA
It's a concern in the sense of "commercial enterprise, entity".
Similarly, it's not "going" in the sense of "leaving" or "going out of business", but "going" as in "ongoing, viable".
So, "going concern" is not a negative thing, meaning "bankruptcy worries" or so, but a positive thing, meaning "viable enterprise".
(Note: not replying to you specifically, but the whole sub-thread :-)
Those say:
* A going concern is a business that functions without the threat of liquidation for the foreseeable future, usually regarded as at least within 12 months. *
Note without the threat of liquidation. So there is no concern, which is what makes the term so confusable.
I would guess that "concern" is somehow a synonym with "company" (which happens to work well in Swedish, for instance), that makes it more sensical.
Source: I know nothing about accounting on any level.
I, um, don't mean that as a snarky comment or anything; it really is in a lot of ways the best explanation. It's weird and fascinating how words slowly shift over time and how ever though "go" or "concern" never necessarily quite "changed their meaning", it still sometimes wanders a little bit and over the course of centuries it can add up to a surprising amount. Phrases sometimes can get "stuck" and survive past their constituent words having their meanings shift away.
And "going" means that it can keep going, that it won't stop because of some failure or limitation.