That is a fair point. In the context of Genesis 1-3, I will explain what I think Genesis 2:1-3 means. In other words, why is it that was included in the story versus left out.
I see a few teachings here.
First, I'll start by using Scripture to interpret Scripture, on key teaching here of the 7 day cycle that concludes with a day of rest in the Sabbath. The narrative tells us something about God's behavior, which is in turn supposed to tell us something about our nature as images of Him. The purpose of Genesis 2:1-3, therefore, is to tell us something about our nature and God's desire manner for of our worship of Him.
From this starting point, it is helpful to see what parallels there are between the 7th day of creation and ceasing to create, and the 7th day of the week and ceasing to work. Here are some things that we see explicitly or implicitly mentioned through Scripture about that:
The purpose of Sabbath was to stay at home together with family and in worship and in community. In the same way, we see God enter the created order in the 7th day, from doing grand things out and about in the cosmos. He takes up residence in the Garden to dwell with Adam and Eve.
This is meant as a blessing to God and man. There is something about our flourishing that happens when we pause from the work of grand things to engage in the relationships of home.
There is a cyclical "seasonality" to the Sabbath rest (remember Ecc.). We are made for work. Technically, Adam and Eve work on day 7. But we are also made for rest. Another way to put this, is that the call to exercise dominion over the earth is to "create worlds (society, art, technology, etc.)," but the call to rest is also to "enter into the worlds we create (to these worlds to create life-giving communities)." But we are also supposed to go back and forth between these things. This also suggests Creatio Continua.
The "total" prohibition of work on Sabbath was not absolute but could be violated for many reasons (e.g. to save a life). This flexibility did not in any way impair the relational/spiritual function of Sabbath. If work = create in this parallel, this suggests that the end of creation was not absolute, but in some rare circumstances it might continue. This to supports the notion of Creatio Continua.
There is a fairly clear quality of healthy human relationships. Functional relationships are often characterized by a give and take of partnership in work (e.g. raising children) where retreat to rest (a date night) is fundamentally important. That back and forth is also that to which this passage speaks. We see this too in our relationship with God, though it is hard to express this in a denomination neutral way.
The statement of rest also is meant to highlight that humans are the pinnacle of creation. On creating us, he feels creation, in the most important senses is completed, because beings capable of reflecting Him in relationship with Him have been made. To call this the solitary purpose of creation seems too restrictive (why then is the galaxy so vast?), but humans do appear to be one "end" of creation. This too is consistent with the notion of God creation a new species now and then (Creatio Continua), because this is not really anything as new or transformative as the entrance of humans into the world.
So I would say that Genesis 2:1-3 is put in the narrative primarily as a message about our nature that is mirrored in God. It lays the foundation for the command of rest, and also teaches something truthful about the human experience. I affirm all those teaching, and I think these teachings are fundamentally more important to everyone (personally, historically, traditionally, early Jewish readers, us today in the Church, etc.) than some sort of precise statement of the mechanisms of creation and its limits.
The good news is that the key parts of this message are reliably extracted from Scripture. That is another sign that we are on the right track, and not substituting a private interpretation for the correct one. This is really the plain reading of the passage.
Does this deny additional meaning regarding God's creation in the physical world too? If we take the day-age view of six days, there are some more parallels worth mentioning.
In day-age, days 1 - 6 are unimaginably longer (hundreds of million to billions of years) than day 7 (which is less than 10,000 years at most). Consequently, there is quantitatively and qualitatively, vastly more creating happening in the first six days. In fact, one could argue (using creationist terms) that during the 7th day, it is so short we only see "microevolution", while the other days we see "macroevolution". Remember, everyone accepts "microevolution" (e.g. antibiotic resistance) during the 7th day.
So perhaps during the 7th day many of the evolution processes are still at work on biological life, and God can still in principle intervene to create things directly or direct evolution as he wishes. However, because the time scale is so much different, this creation is essentially slowed to a standstill compared to the amount of creation that has happened in prior errors.
In this sense Genesis 2:1-3 is an accurate description of the world we see in the evolutionary account. We will see occasional anomalies and elaborations, but God is not creating totally new and different things very frequently (from the perspective of the narrative) at all any more. This might also be seen as Scriptural justification for why we cannot directly observe some of the large evolutionary changes from the past (e.g. the Cambrian explosion, or abiogenesis, or the evolution of a new phyla from scratch).
If we take Walton's view that this applies to a 6-literal day of functional creation in the recent past after long age of material creation, the same spiritual meanings can be extracted. Some of the parallels to the scientific account change, but they are still there.
Notably, one would see the same teachings I've enumerated in this account. That is the beauty of Genesis. It is quite ambiguous about the scientific details, but manages to be extremely robust in its teaching. Whether one is YEC, OEC, TE, or ID, there is a massive amount of overlap in our readings of the teachings of Genesis. The focus is on the differences, which creates the illusion that there is massive disagreement that is consequential.
However, the focus should be on the common ground, which is substantial and theologically significant. The robustness and commonality of the theology we all extract from Genesis should reduces fear about differences in how our interpretations interface with Genesis, and remind us that science was never its point in the first place.
Alongside this Creatio Continua is just a caveat to this story that the end of creation on the 7th day is not a total end. God still does things in this world (and wouldn't you agree?).
Hope that answers your question. I certainly see teaching in Genesis 2:1-3, quite a bit. The fact that I am not caught up on the concordance to modern science helps with interpretation. I'm free to look for the original intent, and what we see in common. This part of the story isn't just a weird quirk with no significance except to make evolution harder to accept. Rather, it is a way of telling the story to teach important theology, and I want to understand that theology.