Willingness to sacrifice oneself for other people you aren't related to, or for ideas, is a distinctive feature of complex intelligence, which has allowed groups to achieve far more than individuals or families could. You could reasonably argue this is the point at which memes, like culture, came to be as important as genes, in understanding humans. We can relate this behaviour to eusociality.
Whether a person does or doesn't do something, or whether they show fear, are poor guides to whether they felt fear. What we tend to care about, is whether someone could be coerced by threats, or pain, or death, into not doing something good or valuable for others, or the opposite, coerced into doing something bad.
Stoic philosophy provides a 'recipe' for not being coerced, and illustrates a major method of philosophy in doing so, reframing our experiences.
“Under no circumstances ever say ‘I lost something,’ only ‘I returned
it.’ DId a child of yours die? No, it was returned. Your wife died?
No, it was returned…Why concern yourself with the means by which the
original giver effects its return? As long as he entrusts it to you,
look after it as something yours to enjoy only for a time – the way a
traveller regards a hotel.” - Epictetus
Does that sound dangerous?
Socrates did not fear death, it is widely considered that he could have accepted exile or lesser punishments, instead of execution. Exactly that lack of fear, unwillingness to be coerced and 'fit in' were the issues he was prosecuted for: What did Socrates teach which lead to his conviction that he spoiled youth and taught other Gods? And I would argue this willingness to live up to his intellectual ideals, to accept 'martyrdom' for them, is exactly what made Socrates paradigmatic in defining what philosophy is: Is Socrates' wisdom intrinsically valuable?
Wisdom is exactly about the process or cultivation of what allows us to not be coerced, by bias or impulse or fear, and instead to act from the integrated centre of our concerns, in facing character tests understood to be above all as solving dilemmas or difficult choices well. Discussed here:
Wisdom and John Vervaeke's awakening from the meaning crises?
So in short, a fearless person can be good for society by being wise, by cultivating wisdom.
When a person overcomes the fear of death they basically lose their
most important instinct that helps and gives them the ability to live.
But, that loss of fear allows them to sacrifice themselves for others, or for ideas. So we need education, and public discourse, that challenges bad ideas, and cultivates wise thinking.
And you say
By ignoring the fear arising from external factors, a person returns
to human’s first stage and their behavior becomes immoral and harmful
to today's society.
Today's society. But what about service to, tomorrow's society? Nietzsche said:
"Man's maturity: to have regained the seriousness that he had as a
child at play" -in Beyond Good and Evil
A recognition that society can be otherwise, that people can behave differently, and a simple demand for fairness, are what the eyes of a child sees. I suggest fearlessness in enacting that, is crucial to a better human future.