This question must be tackled by any Arthurian story with pretensions to depth and significance.
The usual examples that I have come across are related to things like 'peace and prosperity and justice'. Arthur is (supposedly) a Good King because he provides (or at least tries to provide) these - against a alternative backdrop of endemic violence, social chaos, starvation, and arbitrary tyranny.
But - while these outcomes are undoubtedly highly desirable - they are a means to an end - they are a paradise of the farmyard, rather than something especially human.
Therefore Arthur needs also to bring civilization. The stories which use the historical Arthur tend to place him in the incipient 'Dark Age' period after the Romans left England; and therefore can present Arthur as a Roman - who wishes to restore a complex, literate and unified society.
This provides a higher ideal, especially if it is linked to the still existing international civilization of the Eastern or 'Byzantine' Roman Empire - although I have only come across Charles Williams who used this plot device.
So, thus far Arthur can be regarded as aiming to restore the Roman Empire and establish international exchanges of goods and ideas; as well as provide peace prosperity, and justice at home.
But who is to say that any of these things are Good?
After all, that is what most of Western Europe and the Anglosphere has had for the past couple of generations and the result has been a society which lives for distraction and strategizes to destroy itself.
Indeed, the modern Westerner is likely to see the uncivilized, illiterate and violent 'Celtic' and Gothic tribes as more admirable (certainly more 'romantic' - ironic pun intended) than the Romans - more proud, free, spontaneous, artistic and spiritual. The Romans are admired rather than loved; and indeed are perhaps more often hated than admired - so a Roman-restoring King does not have much appeal.
The missing element is, of course, Christianity. In restoring Roman Civilization, and rejoining the Byzantine Empire, Arthur was bringing his people back into Christendom: and that is (or should be) the ultimate reason why he was a Good King.
When writers (like Malory or Tennyson or TH White) set their Arthur legends in Medieval times, instead of the Dark Ages, this profound Christianizing rationale is not available to them - because Medieval England was already Christian; and the artificial and unsatisfactory plot device of The Grail Quest has to be introduced to provide a bolt-on spiritual dimension for Arthur.
Modern people tend to suppose the 'Dark' in the Dark Ages refers to lack of goods and technology, or something material; but of course it actually refers to spiritual darkness.
Modern people forget that the Roman England had been Christian for several generations before the legions departed; and that when Rome fell the capital of the Empire had long since moved to Constantinople. Unfortunately, this meant that Britain was cut-off from (the New) Rome, except by a long, complex and dangerous sea voyage - and the consequence was rapidly catastrophic: materially and spiritually.
But for a (semi-) historical, Dark Age, Romanizing King Arthur; the motivation of re-Christianizing an England slipping back into paganism, and rejoining England to the international Empire of Byzantine Christendom, would represent an ideal spiritual motivation; and one whose potential has barely yet been tapped.
Now, if only I was a storyteller...