Let's not ignore the elephant in the room. UNSC's true purpose and the one it filled well is simple----preventing major powers from starting a world war III.
Now, the politically correct statement would be "peace is achieve by letting everyone's voice be heard and achieve understanding between different nations". Of course, that will also be blatant lie, or at least a theory that does not work well in the real world. In reality, the WORKING method to preserve peace is ensuring people capable of starting a world war have a place and medium that they can use to settle their interests without opening fire. I won't sugar coat it, much of that is done at the expense of smaller and weaker nations/groups. Take the recent Syria case for example, the true nature of the case and Russian/China veto should be interpreted as such:
1. US and EU has interest in Syria in form of remove Assad for another candidate more suitable to US and EU interest.
2. Russia has existing interest in Syria and is in favor of preserving Assad to keep that interest.
3. China has no interest in Syria, but do not wish US/EU to expand its interest in Middle East.
Unfortunately for the Syrians, even though they are the rightful owner of their homeland, their interests are certainly not the ones considered at UNSC. However, at risk of being devil's advocate, I would have to point out even though Syrians in general (Assad and rebels both included) got the raw end of the deal, US, EU, Russia and China walked out with their interests temporarily satisfied. (Or at least settled) And without firing on each other. This will sound cold, but the reality is that whatever damage Syrians can do, it is certain minor comparing to a open conflict between major nations.
Which brought us back to Islamic bloc's suppose ambition to a seat at UNSC, the answer is that unless the Islamic bloc can achieve a political unity and present sufficient force and influence to match the major powers, it is not likely to happen. Similarly, this is why even though India and Japan has attempted to gain access to UNSC for decades, it is still no closer to do so.