Punishment

The situation we are in is not permanent. Every era had its empires and its kings and rulers and they rose and fell. Similarly, today's powerful nations will also fall as this is part of the normal course of history. In fact, in our lifetime, many of us have seen the rise and fall of tyrants. 

The question of why Allah does not intervene to make this happen sooner hinges on the question of the free will of the human being and the balance between Allah's compassion and answering people's prayers, versus the free will that Allah has given to us collectively. On a societal or global scale, divine justice does occur, but it often takes place in the long-term (such as over centuries) rather than in our immediate lives.

From an Islamic perspective, societies are affected by natural/physical laws and higher-level natural laws. For instance, a material or natural law would be that if a government invests in health care, the quality of health in the population will be better. This is true whether people are ethical or unethical, faithful or unfaithful.

In addition to physical natural laws, the Qur'an and hadith speak of higher-level natural laws, which also relate to ethical decisions, for instance, a society that gives up enjoining the good will be afflicted by a tyrant. (Some of these can also be reduced to material/natural laws, e.g. tyranny can be defined in part by clamping down on any sort of opposition or speaking against something and won't emerge in a place where people are constantly enjoining the good.) So we also have the free will to act within those laws but we experience the results collectively.

Basically, the ultimate end of things and seeing divine justice is really just something one needs to be patient for with if one wants to see it dramatically except in some cases where there is some sort of clear divine intervention to answer people's prayers. In the meantime, do what one can do improve the situation we and the world are in, whether it be through actions or even just prayer. 

Here is a good treatment of this question: http://www.askthesheikh.com/did-imam-ali-a-s-really-put-two-men-on-fire-because-they-claimed-he-was-god/

Best wishes

This is a good question, and one that has received a lot of attention in the contemporary era.

Classically, many Muslims held that death is generally the punishment for apostasy (with some exceptions and conditions). Some Muslims today see this more in line with a modern treason law. That is, today, while killing someone for apostasy is considered a violation of human rights, killing someone for treason against their own nation is considered acceptable. This is because, in the past, religion was a primary marker of public identity and deliniation of the state; whereas, in the modern world, religion is considered a private matter and a matter of personal belief, and national identity is considered primary. 

Also, this law is based on hadith. Some people have challenged the authenticity of hadith that say this, because it seems to go against the Qur'anic view that there should be no compulsion in religion; it also seems unusually harsh, since the Prophet had a merciful and lenient character. Other people hold that it may have been appropriate in the time of the Prophet (where leaving the Muslim community would generally mean militarily aiding the enemy) but it is no longer valid today.

So, basically, one can say that, yes, this is a classical view; but it is still a subject of much discussion.

Also, note that even if the classical law is correct, it is not acceptable for a person to go around killing people because he or she thinks they are apostates. 

There are a number of pieces on this on al-Islam.org, which you can read by going to Google and typing "apostasy al-islam.org".