Should a monotheistic God ever be considered good or great?

A monotheistic God is the sole dispenser of justice and for that reason it has got to know everything. To Know everything God has to have quality of omniscience. As such whenever you read an article about monotheistic God, you will find omnipresence, omniscience and omnipotence as essential attributes of monotheistic God.

A being that is omniscient cannot be finite. Because omniscience implies ability to know everything, including infinite numbers (such as all primes). A being that can process infinite numbers has to be infinite itself.

You can make a claim that there may be a special case of a system in which there is one God but that God has finite power. But such a case is not generally held by actual proponents of monotheism. Further such a case questions the very notion of an all powerful being.

I am sure you at least agree that a monotheistic God cannot be born. Any God who has a birth can be born from an outside agency. Outside agency giving birth to God will be another God. But in such a case basic tenets of monotheism is contradicted. So a monotheistic God is eternal (unborn) by its nature. Concept of eternity is very closely related to the concept of infinity.