Loge is not an interesting character IMO because he has no skin in any of the games of the "Ring" (and this is a rather implausible stance within the world of these operas). This seems more evidence that he isn't really a god but, like Erda, more an elemental spirit. (The similarly elemental Rhinemaidens do have skin in the game because their gold got stolen.) He doesn't seem to care for anything, he seems unaffected by the weakening due to lack of Freya's apples etc. Consequently, he fades to merely instrumental flickering in the magic fire music, two operas before the other gods fade. When water and fire consume Valhalla and the gods at the end, I wouldn't see this as "Loge having won" but as further indication of disenchantment, from now on water is water and fire is just fire, not Loge.
I agree with some of what you wrote and disagree with other parts. You bring up Erda, which is a really interesting case; she and the Norns (which are little more than an extension of Erda herself) are the only actual deity-like beings in the Ring; Wotan is basically a human with a spear and some golden apples. Also, Floßhilde mentions a "father": "Vater warnte vor solchem Feind" / "Father warned us of such a foe"; this father doesn't seem to be Wotan, since he has only peripherally heard of the Rheinmaidens or their gold, so this father figure might be a counterpart to Erda. He isn't really a god, but that's because we know he is only half immortal. (Alberich mentions Loge was once his friend; I don't think it's mentioned explicitly in the libretto if Loge is half Nibelung or what exactly his ancestry is). This makes him, if anything, farther from being Erda-like, in my view; he's less of a god than the gods, and even they are really not all that god-like.
But Loge doesn't vanish at the end. His music appears in
Siegfried, for example at "fühltest du nie im finstren Wald?" Also his music is (for obvious reasons) important for the ending of
Siegfried, starting from the Siegfried/Wanderer confrontation and the orchestral interlude which follows. He's mentioned by name in the Norn scene, and we find out that he had openly defied Wotan between
Das Rheingold and
Die Walküre by turning into fire and threatening Wotan's spear. At the end of
Götterdämmerung, we hear his music again as Brünnhilde picks up a torch at "Fliegt heim, ihr Raben," and she explicitly bids Wotan's ravens to send Loge back to Valhalla. As she finishes her monologue and sets the pyre aflame, we hear Loge's music again. Presumably, when Loge does return to Valhalla, he (being the demigod of fire as well as of wit) is the force behind its conflagration, having made up his mind as to whether he will burn the place down as he pondered doing at the end of
Das Rheingold. This is the "Loge having won" proposition you mentioned in your post. In the source mythology, Loge/Loki is quite a different character, but he does end up waging war on the gods in the end. But even leaving that aside, I think that Wagner leaves enough evidence to suggest that Loge is an important character for the entire cycle.
