I have hear folks complain about WoW’s handling of timelines for a long time but… honestly, it is actually pretty good. Because it is consistent in that we can affect other timelines, we can bring things in from other times and also put things into other timelines. The job of the bronze dragonflight is to essentially be custodians that enable timelines to continue unimpeded, but that doesn’t mean they can’t be changed. This is what we got confirmation of when interacting with the Infinite dragonflight in Dragonflight.
For a better resource, watch this video by Minutephysics:
WoW’s type of time travel is a combination of both multiple dimensions where we can interact with objects back and forth completely. But also that different dimensions can be at different stages in time, meaning that they have progressed as they would normally because that’s what happened in their timeline.
In essence, we have a mixture of Harry Potter and Back to the Future types of time travel (with a slight bit of Primer in there because of the need of a functional portal), and the timelines reflect that. In a dimension where the timeline progressed differently, it progressed differently and continues from that point forward. But in terms of how we interact with a timeline, of course it happens one way or another because that is what happened. Not necessarily in our dimension or in such a way where we could see it happening, but characters like Broxigor and items like the Dragonsoul is why these things work.
As long as a timeline continues as it is supposed to, the Bronze flight’s mission is upheld. And that is also reflected in how we are able to interact with different timelines and different dimensions both in-universe and in-game.
So… to answer your question of,
The timelines doesn’t disappear, but you do remain dead in that timeline dimension. At most when a “timeline disappears”, it simply means it is now inaccessible through more conventional means of travel.
Argus acted as a Primer-styled time machine, much like how the Twisting Nether also acts as a Primer. Effectively yes, there’s infinite versions of everything in the Warcraft universe but that’s also what makes the timeways so unstable when messed with.
So for certain infinites, it is likely that the simple answer is that Demons can make use of the Twisting Nether as a Primer. Similarly how the Dark Portal acts as a Primer to other Dark Portals, and the Timeways converge in the Caverns of Time which acts as a Primer for other timelines. Is it possible as a direct result to find another Argus? Sure… if we could get to it. Which we might not be able to because we have now lost Argus, and we have no ideas whether we can go to Argus when we have no Argus ourselves.
Of course most of this gets hand waved away but because of how Warcraft has handled both time travel and multiple dimensions … it is honestly still consistent with itself. Not perhaps as logical as one would prefer it to be but, still consistent as far as we aware … and we can only become aware of its inconsistency if we were to travel to Argus again - either before, after, or during its corruption.