Tennyson's “Ulysses” is written from the point of view of the king of Ithaca himself, which gives us a privileged insight into his thought processes. As Ulysses is talking about himself to himself, he is extremely candid. That being the case, we are able to take his words largely at face value, which makes it a lot easier to evaluate him as a man and as a king.
As a consequence, we could argue that Ulysses really isn't a very good king. He may be a brave warrior with a series of heroic deeds to his name, he may have traversed virtually every square inch of the known world on his many adventures, but when it comes down to being king of Ithaca, he leaves quite a lot to be desired.
The evidence for this argument comes from Ulysses's stated desire to leave his people behind and embark upon new adventures, despite his advanced years. In the very first lines of the poem, we see just how dissatisfied Ulysses is with the role of monarch and how much it makes him want to head out to sea once more:
It little profits that an idle king,
By this still hearth, among these barren crags,
Match'd with an aged wife, I mete and dole
Unequal laws unto a savage race,
That hoard, and sleep, and feed, and know not me.
I cannot rest from travel.
As Ulysses readily confesses in the first line, he is an idle king. It's surely not unreasonable to suggest that this is not the hallmark of a good king. Nor is it the sign of a good king that he should harbor such contempt for his own people.
Yet that is precisely the attitude that Ulysses expresses when he refers to his own people, the people of Ithaca, as “a savage race.” What's more, he frankly admits that he dispenses unequal laws unto them, a reference perhaps to an unjust legal system over which he himself presides.
Clearly, Ulysses is getting bored with being king. And so it's not surprising that he should want to leave Ithaca behind and head off on new adventures, “to strive, to seek, to find, and not to yield.” Although this attitude to life makes him more recognizably human, it does, at the same time, make him less of a king.