Many arguments for theism don’t establish an omni-max entity, i.e. one that is omnipotent, omniscient, and perfectly good. One could construct a version of the moral argument to argue that a perfectly good being grounds objective moral values (where God is the Good), but that’s pretty much the exception, at least with respect to the pro-theism arguments I might normally discuss.
Consider for example the Leibnizian cosmological argument for God, where I argue for a transcendent personal cause (on the grounds that the physical universe is contingent and thus needs an explanation for why it exists rather than not). The kalam cosmological argument similarly argues for a transcendent personal creator (on the grounds that the physical universe began to exist and thus needs a cause). Granted, creating the universe is a big job, but why an omnipotent God instead of a merely enormously powerful one? This is where the role of simplicity helps.
In an earlier article I argued for the idea that all else held constant, the simplest explanation is the best and most probable one. One aspect of simplicity is Ockham’s razor which suggest we do not multiply explanatory entities beyond necessity. So when positing a transcendent personal cause of the universe, it is simpler to posit just one being as the cause rather than many of them.
Another facet of simplicity is this. Let S (for simple) and C (for complex) be placeholders for mathematical entities/relations. A mathematical entity/relation S is simpler than another one C if S can be understood by someone who does not understand C but C cannot be understood who does not understand S. For example, 0 and 1 (S) are simpler than 2 (C), 2 is simpler than 3, and so forth; you cannot understand the notion of 2 rocks (C) without first understanding the notion of 1 rock (S). In Simplicity as Evidence of Truth, philosopher Richard Swinburne says that an infinitely large quantity is graspable by someone who hasn’t grasped a very large number. Quoting him:
One does not need to know what a trillion is in order to understand what is the infinitely long or lasting or fast. It is because infinity is simple in this way that scientists postulate infinite degrees of quantities rather than very large degrees of quantities, when both are equally consistent with the data. The medieval postulated an infinite velocity of light, and Newton postulated an infinite velocity for the gravitational force, when in each case large finite velocities would have been equally compatible with the data then available measured to the degree of accuracy then obtainable.So why prefer an infinitely powerful God rather over a merely enormously powerful one? One reason is simplicity; an infinite quantity of power is simpler than a merely very large quantity of power. So all else held constant, it’s simpler to posit an infinitely powerful transcendent personal cause. To quote Richard Swinburne from his book The Existence of God:
A finite limitation cries out for an explanation for why there is just that particular limit, in a way that limitlessness does not…scientists have always preferred hypotheses of infinite velocity to hypotheses of very large finite velocity, when both were equally compatible with the data. And they have always preferred hypotheses that some particle had zero mass to hypotheses that it had some very small mass, when both were equally compatible with the data. There is a neatness about zero and infinity that a particular finite numbers lack. Yet a person with zero powers would not be a person at all. So in postulating a person with infinite power the theist is postulating a person with the simplest kind of power imaginable. A person with literally no power would not even have the ability to think, much less create a universe. The simplicity of zero and infinity can also be granted to “nothing” and “everything.” To illustrate, scientists tend to believe that the physical laws that apply to all observed electrons (a tiny fraction of all electrons in the universe) also apply to every electron in the universe, even though a more localized influence of physical laws would be equally compatible with the data. God knowing everything (and thus having infinite knowledge) is not only simpler than knowing a merely large finite quantity of stuff, but knowing all that can be known also seems to be the magnitude of knowledge most consonant with omnipotence. So all else held constant, it is simpler and better to posit infinite intelligence and infinite knowledge here.
God is an infinite power that all other power ultimately derives from (both physical and volitional; e.g. God delegated some of his power to us humans when he gave us power over our own actions). There is a kind of elegant simplicity in the theory that all power ultimately originates from some ultimate source.
Something similar could be said for knowledge. God, an entity that knows everything, is the ultimate source of knowledge and warrant. Some of our beliefs are properly basic (beliefs that are justified but not justified on the evidential basis of other beliefs), and theists believe that God designed us (by evolution or otherwise) in such a way that when our cognitive faculties are functioning properly we intuitively apprehend certain elementary truths about logic, mathematics, and morality. Our knowledge of such basic truths ultimately originates from God himself. By my lights, there is likewise an elegant simplicity in the theory that all knowledge ultimately originates from some ultimate source.
I suspect on some level humanity’s attraction to simpler explanations is one of the motivating factors for us humans to posit an omnipotent (infinitely powerful) and omniscient (infinitely knowledgeable) being. At any rate, the principle that we should rationally prefer simpler explanations ceteris paribus does help the theist in arguing for an omni-max God.
 Swinburne, Richard. Simplicity as Evidence of Truth (Milwaukee, Wisconsin: Marquette University Press, 1996), pp. 33-34.
 Swinburne, Richard. The Existence of God, 2nd edition. (New York, New York: Oxford University Press, 1996), p.97