Yes, these are obviously common arguments.
For a couple of decades post WWII, there was a general consensus among philosophers that this - or something like it - was successful as a deductive argument. As you have phrased it here, the argument is not valid. A better formulation would be:
(1) If a perfectly good, omnipotent God exists, then the degree of suffering that we see would not exist.
(2) But the degree of suffering that we see exists.
(3) Therefore, a perfectly good, omnipotent God does not exist.
That argument is valid (ie, if the premises are true, the conclusion must be true). As I said, there was a time when most people thought that the premises were true, and that the conclusion is therefore true (and actually demonstrated to be true). Today, few philosophers accept this. The reason is that we cannot really know premise (1) to be true. There could be some reason, unknown to us, why God would permit the degree of suffering that we see. Even if we can't think of such a reason we can't rule out that it exists.
So the form that this argument generally takes today is an inductive argument, that is, one that is supposed to show that its conclusion is probable. Such an argument might run like this:
(1) Probably, if a perfectly good, omnipotent God exists, then the degree of suffering that we see would not exist.
(2) But the degree of suffering that we see exists.
(3) Therefore, a perfectly good, omnipotent God probably does not exist.
That seems to me to be a pretty good argument. Of course it doesn't prove that God exists, but then, as I say, most substantial claims about the world cannot be proved. The strength of the argument also depends upon how strong you can make that "probably" in premise (1), and the justification you can provide for it. But that seems to me not enormously difficult to flesh out.
Arguments of this kind, in my opinion, are extremely poor. For one thing, both of the first two premises are false - there exists evidence both for and against God. The third premise seems pretty questionable to me. Perhaps a world with God would be simpler than one without God, because God is a very simple being, and can serve as an explanation for many things. The world without God, then, would have to have many, more complex, explanations for those things, and thus be overall more complex.
However, the weakest element of arguments of this kind is the supposition that simpler explanations are always to be preferred. This is certainly a common assumption in science - although it is one that is very rarely defended, surprisingly. In fact the only book-length defence of this principle that I have been able to find (and I have researched this quite carefully recently) is by Richard Swinburne - who uses the principle as a central premise in his argument for God. And it's a pretty short book too. But there are important philosophers of science today who argue that in fact the principle doesn't exist at all. Elliott Sober, for example, argues that there is no general principle of simplicity. Rather, different branches of science have certain reasons, local to those branches, why simpler hypotheses are to be preferred, and it's just a sort of coincidence that this is often the case. Furthermore, there are many cases where simpler hypotheses are not to be preferred. Most pertinently to this discussion, I don't know of any good argument that shows why, in the question whether there is a God or not, the simpler hypothesis is to be preferred - even assuming we can identify which hypothesis actually is the simpler. Indeed, the fact that people can't even agree whether theism is simpler than atheism or vice versa is one thing that suggests to me that this whole issue is an enormous red herring.
For a couple of decades post WWII, there was a general consensus among philosophers that this - or something like it - was successful as a deductive argument. As you have phrased it here, the argument is not valid. A better formulation would be:
(1) If a perfectly good, omnipotent God exists, then the degree of suffering that we see would not exist.
(2) But the degree of suffering that we see exists.
(3) Therefore, a perfectly good, omnipotent God does not exist.
That argument is valid (ie, if the premises are true, the conclusion must be true). As I said, there was a time when most people thought that the premises were true, and that the conclusion is therefore true (and actually demonstrated to be true). Today, few philosophers accept this. The reason is that we cannot really know premise (1) to be true. There could be some reason, unknown to us, why God would permit the degree of suffering that we see. Even if we can't think of such a reason we can't rule out that it exists.
So the form that this argument generally takes today is an inductive argument, that is, one that is supposed to show that its conclusion is probable. Such an argument might run like this:
(1) Probably, if a perfectly good, omnipotent God exists, then the degree of suffering that we see would not exist.
(2) But the degree of suffering that we see exists.
(3) Therefore, a perfectly good, omnipotent God probably does not exist.
That seems to me to be a pretty good argument. Of course it doesn't prove that God exists, but then, as I say, most substantial claims about the world cannot be proved. The strength of the argument also depends upon how strong you can make that "probably" in premise (1), and the justification you can provide for it. But that seems to me not enormously difficult to flesh out.
Arguments of this kind, in my opinion, are extremely poor. For one thing, both of the first two premises are false - there exists evidence both for and against God. The third premise seems pretty questionable to me. Perhaps a world with God would be simpler than one without God, because God is a very simple being, and can serve as an explanation for many things. The world without God, then, would have to have many, more complex, explanations for those things, and thus be overall more complex.
However, the weakest element of arguments of this kind is the supposition that simpler explanations are always to be preferred. This is certainly a common assumption in science - although it is one that is very rarely defended, surprisingly. In fact the only book-length defence of this principle that I have been able to find (and I have researched this quite carefully recently) is by Richard Swinburne - who uses the principle as a central premise in his argument for God. And it's a pretty short book too. But there are important philosophers of science today who argue that in fact the principle doesn't exist at all. Elliott Sober, for example, argues that there is no general principle of simplicity. Rather, different branches of science have certain reasons, local to those branches, why simpler hypotheses are to be preferred, and it's just a sort of coincidence that this is often the case. Furthermore, there are many cases where simpler hypotheses are not to be preferred. Most pertinently to this discussion, I don't know of any good argument that shows why, in the question whether there is a God or not, the simpler hypothesis is to be preferred - even assuming we can identify which hypothesis actually is the simpler. Indeed, the fact that people can't even agree whether theism is simpler than atheism or vice versa is one thing that suggests to me that this whole issue is an enormous red herring.
