The discussions earlier on why UNSC expansion has not taken place, even though it has been over 70 years since the creation of the UN, already hits on most of the explanations for why the current P5 still retain their seats and what the principal geopolitical purpose of the UNSC (and the UN in general) is: serving as an established forum for the P5 to engage in diplomacy rather than resort to military means to resolve disputes between one another, particularly in the nuclear age. As such, the UN's core purpose has been this above everything else, and to fulfill it at all costs.
The United Nations exists in the shadow of the League of Nations, which collapsed precisely because Japan (and then the entire Axis) withdrew after the League condemned its invasion of Manchuria. The United Nations structure as it exists today, in spite of all the associated injustices and failures of such a framework, was crafted that way solely to prevent it from the same path that the League went down.
Following WW2, the UNSC had been devised as a victor’s prestige club by Roosevelt for his "Four Policemen" world government vision, that is, to keep the Axis down and to codify a global power hierarchy where the Allies are enshrined on top by international framework. However, the idea of the UN’s fundamental purpose as a place for the major powers to mediate disputes wasn’t fully appreciated until the Korean War, where the so-called “UN Command” coalition under US control catastrophically miscalculated and forced China’s entry into Korea. Through a lack of diplomatic channels to China and having barred even an informal Chinese presence in the UN, China had to convey its ultimate warning through the Indian ambassador. The newborn collective “United Nations,” the nascent international order, subsequently had its baby teeth broken in by the People’s Volunteer Army's counteroffensive after reaching the Yalu. This revealed the price of an international order that ignored the reality on the ground of power conditions and it was only after China’s intervention that the US permitted an unofficial Chinese delegation to the UN.
As such, international law and international diplomacy are, fundamentally, pantomime acts that only endure because the major powers hum along to the tune. In other words, the international legal order under the UN Charter is the allegorical emperor that has no clothes and it can only walk around in confidence because those major powers pretend to see that it is clothed. These are the material conditions that the UN endures upon and the reason why the major Allied powers were given and retain P5 status to this day. It is indeed unjust to the rest of the world how the entire framework serves to assuage these major powers in the same way that the League could have only survived if it appeased the Japanese following their bloody atrocities in illegally invading China. Justice, however, is besides the point.
As for reform and expansion, the real reason why countries like India haven't been admitted into the P5 is because elevating a country into UNSC permanent seat status ensures, through initiation into this club, that the status of that country is enshrined into the international power hierarchy. What does this mean in practical terms? It means that such a country no longer has to appeal to one of the P5 (usually Russia or the US for India) to protect its interests in the UNSC. It means that such a country itself becomes a new unbeholden powerbroker in the UNSC such that its views need to be satisfied to prevent vetos or stonewalling and that non-UNSC countries are able to come to it as an alternative to the P5 to secure their own interests, which obviously then deprives the latter of such leverage. These are significant enough privileges that countries actively campaign with serious effort for merely rotating UNSC seats and the P5 in the past 70 years have expressed no interest in extending such privileges permanently. India, in particular, is said to be explicitly blocked by China, which means the other four (particularly the US and Russia) are free to dangle their “support" for its candidancy like a carrot. The fact that their support to this point only extends as far as it lets them contrast their “generosity" with that of “uncooperative" China for virtue signalling purposes shows that it has been fundamentally insincere.
Additionally, discussions on UNSC expansion nearly always fail to appreciate the views of those many countries who know they don’t have a chance themselves of inclusion through such reform including the neighbors and rivals of would-be inductees like India. India’s inclusion would confirm its hegemonic status in South Asia, a betrayal of Pakistan on China’s part if the latter agreed, and deeply problematic for local neighbors like Bangladesh, Nepal, Sri Lanka and the Maldives, not to mention even SEA, as it would subordinate them and diminish their diplomatic autonomy through Indian threats of veto in conflicts of interest. This is why such countries formed the “Uniting for Consensus” bloc and for them, it’s a case of, as the saying goes, "better the devil you know." Such concerns exist in the case of every single would-be candidate. As such, UNSC expansion is opposed both from the top and from below with only the middle few truly enthusiastic about it. The concluding assessment is that the UNSC was created in the paradigm shift of WW2 and it will take another paradigm shift for reform of the P5 structure, which can sustain itself currently through indefinitely appealing to inertial tradition as the victors of the war, to be seriously considered.
