If God exists, then an ability to stop these disasters means he isn't omnipotent or caring and thus unworthy of our worship.

If you believe that God causes these things as a punishment for sin, then you run into very problematic ground as a) these disasters effect both righteous and unrighteous b) you have to conclude in the concept of a jealous, angry and dispicable God that is again, not worthy of worship or at all aligned to the concept of God as declared through Jesus (should he also have existed). I.e the common issues you run into when you read the OT or BoM.

The really interesting questions however arise if you assume that God could have intervened but chose not to.

We often hear about God:

* allowing natural laws to prevail (ok, but would it be too much trouble to stop big disasters like this and doesn't answer why he allows?)
* or that he allows the agency of man to prevail (understandable in the context of leader's poor decisions leading to wars and related suffering, but not in context of natural laws)
* and also that this earth life is but a small dot in the grad scheme of eternal time (even if true, doesn't in my mind really help alleviate a lot of very real, significant suffering).

So, if you still believe in God, how do you comfortably square his allowance of widespread natural disasters and the concept of a loving sky father?

My beef with the Sky Daddy stems from having seen places such as Haiti, both before and after the quake.

The squalor was awful before the quake when I was there in 2009. The cruelty of the ruling plantation class, the connivance of the American embassy in perpetuating them, the utter hopelessness of the wretched poor trying to eke out a living after being thrown off their land caused by the dumping of subsidized American rice (which they can't compete with) struck me.

Imagine the place after the quake where all these wretches lived in cinderblock hovels, if they were lucky, perched on sides of hills which collapsed into landslides. I was there in the summer of 2010 and most of the rubble was still there after 8 months!. The US was mostly concerned about controlling the nearly non-existent government while organizing fraudulent, sham elections which left out the majority of the population (as represented by the exclusion of the most popular party, Fanmi Lavalas).
There are hundreds of thousands of people there who cannot move away from the island and yet have to live under plastic sheets in areas without sanitation, subject to eviction by landlords. There are no jobs. No schools. No hope. Only rich NGO types running around in expensive SUVs, doing only a bit. Not every one of them is Sean Penn. Most of the NGOs there are living off the aid meant for the people. Very little of the money donated has actually gone to the people. It is the NGOs, not the token, nearly invisible government, that is mishandling all the money. The Haitians' misery is big business for many NGOs. Something should be done but is not. The people there are imprisoned on their third of the island and are ignored by the world ... and by a supposed God.

No, if the Sky Daddy really existed, (s)he or it would make sure those people wouldn't be so miserable. You only need to read the history of Haiti to realize exactly why the place is so poor (incredibly cruel slave plantation system insituted by the French, the takeover by mulatto elites who despise the Black majority, the embargo by the slave-holding US during the first decades, the forced reparations to France for the lost of their slaves, 90,000,000 gold francs, the US occupation of Haiti which then trained a murderous army to keep the people down, the Americans interests in, and the Commies out, the US supported dictators and CIA-directed coups).
Truly, if God existed or cared about his/her children, there would be intervention. And I am only talking about one, poor, benighted country done in by France and the US. There are the cases of the Holocaust, Guatemala massacres in the 1980s, Congo, the Taiping Rebellion in China, etc. as well as natural disasters in Bangladesh, etc. Why did God fail to intervene there as well? How many people's faith were strengthened and how many had it quashed?
In conclusion, we are here on our own in this world. The explanation that these injustices or calamities, natural or otherwise, are only meant to test our faith, is pure taurine faeces for me. As a human being, we can only try to take care of others so that they might not suffer so much but the main obstacle to that is greed, stupidity, and sheer evil on the part of our fellow humans, so-called Homo sapiens. Money trumps justice. Profit before principles. Idiocy is still stronger than Enlightenment.

This is one of the reasons why am I an athiest. That and I can't really see the difference between God and a child's imaginary friend. Except this imaginary friend seems to mostly reflect all the worst things about human nature.