To be clear when I ask about the "significance" of alewives I'm wondering both what they actually were in Mesopotamian society and how other people would see the role. Would it be read as a rags to riches type story or was alewife a prominent job socially?
Great question! Kubaba (or Kugbau) is an interesting case, and not just because she's the only queen mentioned in the Sumerian King List (SKL). A bit of background on the SKL: there are several different lists from various cities known, each with slightly different orders and names. They seem to have been political texts more than just records: they served to legitimise city states' rule over others by providing a precedent for expansionist conquest. (In the sense of, "well, you see, the rightful kingship over Sumer keeps changing hands, it's Uruk's/Ur's/Nippur's/Isin's/Larsa's turn now.")
But you're right - Kubaba the alewife (or brewer/innkeeper) is an unusual entry. It should be kept in mind that the SKL goes so far back into the mists of history that it was ancient even to the Sumerians, so it's unclear to what extent some names on the list are even historical. Kubaba may well have been historical, though, and some kings listed before her are attested in inscriptions elsewhere. For her, sadly, we don't have any contemporary external evidence; we've just got this entry. So since we don't have any contemporary assessments of her rule (or even many references to it outside the SKL) there are two things we can explore further to answer your question:
What was the role of female brewers in ancient Sumer?
How was Kubaba perceived in later Mesopotamian texts?
Part the First: Female Brewers in Mesopotamia
There's a lot that we can say about this, but I'll try to keep it compact. The Code of Hammurabi (CoH) lists a few rulings regarding innkeepers: if they don't report seditious activity in their inn, they're to be put to death. If they overcharge their customers for the beer that they sell, they're to be put to death. If a particular kind of priestess quits her job and opens an inn... you guessed it. What's interesting here is that the CoH assumes that innkeepers are female (or at least it only discusses female innkeepers), so we can assume that the job more generally was considered to be a woman's job. We see this perhaps reflected in one of the Gilgamesh Epic's supporting characters - the goddess Siduri, the brewer of the gods, is effectively a deified version of this role. Going back to Hammurabi, the fact that he acknowledges the role in four separate rulings - one of which involves sedition - suggests its importance to Mesopotamian society. That's not to say necessarily that it was considered a high-status role during this time, but it helps demonstrate that women in Mesopotamia weren't exclusively relegated to the household.
As a brief excursus - recognising certainly that rulership was generally restricted to men - it has long been recognised that women in Mesopotamian society enjoyed relatively many liberties to men in terms of economic activity and civil liberty. We can see this again in the CoH - divorce arrangements benefited men and women rather fairly, and protections for women in abusive relationships existed (at least on paperclay). More broadly, we have significant evidence of women being trained as scribes and writers (famously Enheduanna, who so far is the oldest known author), and in fact the patron deity of scribes was the goddess Nidaba. Keeping in mind that scribes and priests (which Enheduanna was both, appointed to the supreme priesthood of Sîn by her father Sargon of Akkad) were some of the highest-ranking officials in Mesopotamian society, it certainly shouldn't come as a surprise that we find influential women at court and even as queens. Even much later on, in the Neo-Assyrian empire, Sennacherib's wife Naqi'a was instrumental in securing the kingship for both her son Esarhaddon and her grandson Ashurbanipal, demonstrating her significant power at court.
Further reading for the above: Raign, "Finding Our Missing Pieces—Women Technical Writers in Ancient Mesopotamia", Journal of Technical Writing and Communication 49 (3), 2019. Not an assyriological paper but contains a very helpful overview.
Part the Second: Kubaba's reception in cuneiform texts
Perhaps frustratingly, perhaps suggesting that her position as queen didn't raise too many eyebrows, the evidence for later reception of Kubaba is scant. Karen Radner's excellent paper on Kubaba, "Kubaba und die Fische" ['Kubaba and the fish'], traces two separate traditions in the Neo-Babylonian and Neo-Assyrian empires.
The first is essentially a series of cuneiform fragments part of the Weidner Chronicle, a late text that expands on the SKL. This text fits in the broader genre of cuneiform commentaries, where later scribes would expand on (or explain through other means) difficulties in texts that at that point were part of their tradition - this one simply provides further narrative around the relatively dry entries of the SKL (sort of like the biblical book of Chronicles does for Samuel and Kings). It discusses how Kubaba became queen, and details her efforts to properly reinstate the fish sacrifice in the sanctuary of Marduk (the city god of Babylon), for which she was appointed ruler. (Interestingly, the Weidner Chronicle lists jobs for some other kings before they became king too; e.g. Utu-hegal, a fisherman, became king in Uruk.)
The other strand is a small cuneiform text known as the 'Kubaba Omen', a text detailing how certain omens should be interpreted as signs of future. This text takes a rather less positive view of its subject: it cannot be a coincidence that it extremely specifically regards intersex miscarriages, and that the omen (named for "Kubaba, who once ruled") is taken to mean "the ruin of the kingdom; a eunuch will rebel against the king."
Radner's paper (in German): Radner, "Kubaba und die Fische" in Von Sumer bis Homer, AOAT 325, pp. 543-556 (2005).
In conclusion, we have two drastically different approaches to the sole queen of the SKL. One the one hand, a scribal tradition that apparently wasn't too surprised that a woman could rule Sumer, perhaps on the basis that women in Mesopotamia could be entrepreneurs, highly-trained scribes and priests, and hold significant power at court. On the other hand, a single omen text that clearly saw Sumerian queenship as an improper breach of gender roles.
I should mention here that it is often difficult to gauge exactly how ordinary people perceived other ordinary people, since the only extensive texts we have were written by elites. Still, the fact that women could and did participate fully in these circles (at least in the second millennium BCE) suggests that perhaps the curious thing is that she became ruler; not that she was a woman who held power.
PS: Kubaba eventually became Kybele... but that's beyond the scope of this question!