Why are "Fear and Shame" listed among the beautiful cetasikas?

In the Abhidhamma, regret and remorse over the past is considered an unwholesome mental factor.

Worry (kukkucca) is remorse, brooding, and repenting over evil acts done in the past or good acts left undone.

The following theme for reflection from AN 5.57 (quoted below) can prevent the arising of unarisen unwholesome states. It encourages shame of evil (hiri) and fear of evil (otappa), which are mentioned as beautiful mental factors in the Abhidhamma.

So, remorse and regret over the past is unwholesome. But shame of evil and fear of evil, or basically moral shame (hiri) and fear of wrongdoing (otappa), for the future, is wholesome.

“And for the sake of what benefit should a woman or a man, a householder or one gone forth, often reflect thus: ‘I am the owner of my kamma, the heir of my kamma; I have kamma as my origin, kamma as my relative, kamma as my resort; I will be the heir of whatever kamma, good or bad, that I do’? People engage in misconduct by body, speech, and mind. But when one often reflects upon this theme, such misconduct is either completely abandoned or diminished. It is for the sake of this benefit that a woman or a man, a householder or one gone forth, should often reflect thus: ‘I am the owner of my kamma, the heir of my kamma; I have kamma as my origin, kamma as my relative, kamma as my resort; I will be the heir of whatever kamma, good or bad, that I do.’
AN 5.57

And from Iti 42:

"Bhikkhus, these two bright principles protect the world. What are the two? Shame and fear of wrongdoing. If, bhikkhus, these two bright principles did not protect the world, there would not be discerned respect for mother or maternal aunt or maternal uncle's wife or a teacher's wife or the wives of other honored persons, and the world would have fallen into promiscuity, as with goats, sheep, chickens, pigs, dogs, and jackals. But as these two bright principles protect the world, there is discerned respect for mother... and the wives of other honored persons."

Those in whom shame and fear of wrong
Are not consistently found
Have deviated from the bright root
And are led back to birth and death.

But those in whom shame and fear of wrong
Are consistently ever present,
Peaceful, mature in the holy life,
They put an end to renewal of being.
Iti 42

In addition to the answers above it might help to reflect on the opposites of Hiri and Ottappa (Ahirika and Anottappa). Just as Hiri and Ottappa arise in all wholesome mental states, Ahirika and Anottappa arise in all unwholesome states of mind.

Ahirika (shamelessness / immodesty) has a characteristic of “no disgust over misconduct”, a function of “doing evil without shame”, a manifestation of “not shrinking away from evil” and a proximate cause of “lack of respect for self”. Just as a pig is not ashamed to roll in sewage, the mind is not disgusted with unwholesome actions, speech or thought. The Buddha said to his son, “Of anyone for whom there is no shame at intentional lying; of him I say that there is no evil he cannot do. ‘I will not speak a lie, even for fun’ – this is how you must train yourself”. In other words, there is no room for “white lies”. To check if there is Shamelessness in the mind, ask yourself, “Is this the kind of Mental State that could arise in an Arahat?” or ask yourself, “Would I be proud if my thought were reported as a headline in tomorrow’s newspaper?”

Anottappa (recklessness / lack of moral dread) has a characteristic of “no dread over misconduct”, a function of “doing evil without dread”, a manifestation of “not shrinking away from evil” and a proximate cause of “lack of respect for others”. Just as a moth gets attracted by fire and is burned, Recklessness is unaware of consequences, gets attracted by the unwholesome and plunges into the danger zone. To check if there is Recklessness in the mind, ask yourself, “Is this Mental State going to be the wind under my wings to lift me up, or the weight around my neck to drag me down?” or ask yourself, “What kind of kamma is this Mental State creating?”

Fear and shame I believe are referring to the words hiri and ottappa. Hiri-ottappa is not fear and shame in the ordinary sense of these words but it refers to something like the self-correcting concern that a stream enterer has even for making minor transgressions that could hinder progress towards Nibbana. This concern comes through understanding that these actions really are unskillful and having seen a glimpse of Nibbana and having unshakable confidence in the Buddha makes this individual shameful of committing even minor acts that are unskillful. Similar to how a minor blemish on an otherwise dirty piece of cloth doesn't really make a difference, a stream enterer on the other hand sees his/her weaknesses as a blemish on a pure white cloth that needs to be erased. Hiri-otappa is one of the reasons why a stream enterer is on a path of continual improvement that inevitably leads to Nibbana.