It is not only the speaker of "Thanatopsis" who has experienced the fear of death but the reader whom he is addressing. Note that the speaker, presumably William Cullen Bryant himself, says:
Of the last bitter hour come like a blight
Over thy spirit, and sad images
Of the stern agony, and shroud, and pall,
And breathless darkness, and the narrow house,
Make thee to shudder, and grow sick at heart;--
He is obviously assuming that his reader has experienced the same feelings he has experienced himself. This is understandable--at least to an older person--because the fear of death is universal. It is also universally disheartening, because it makes people wonder what is the point and purpose of living and achieving if everything is going to be taken away at some unspecified but unavoidable date in the future. Shakespeare expresses this universal fear of death through his young character Claudio in Measure for Measure.
Ay, but to die, and go we know not where,
To lie in cold obstruction and to rot,
This sensible warm motion to become
A kneaded clod; and the delighted spirit
To bathe in fiery floods, or to reside
In thrilling region of thick-ribbed ice,
To be imprison'd in the viewless winds,
And blown with restless violence round about
The pendent world; or to be worse than worst
Of those that lawless and incertain thought
Imagine howling: 'tis too horrible!
The weariest and most loathed worldly life
That age, ache, penury and imprisonment
Can lay on nature is a paradise
To what we fear of death.
Children are immortal like the Greek and Roman gods because they have not yet realized that they are mortal. Death is something that is so far away that it will never happen.
Literature is full of poems and stories about subjects connected with human mortality. Edgar Allan Poe seems to have been obsessed with the same ideas about death that Shakespeare expresses in Measure for Measure. Poe's famous story "The Masque of the Red Death" is all about the fact that death is inescapable. Shakespeare's Hamlet also contains many speculations on the subject of death, including Prince Hamlet's morbid thoughts when he is handed the skull of the court jester Yorick.
Sir Francis Bacon wrote one of his best-known essays "Of Death." He says:
It is as natural to die, as to be born; and to a little infant, perhaps, the one is as painful, as the other.
What is most significant about Bryant's "Thanatopsis" is that he does not attempt to offer the traditional Christian consolation for death, which is the assurance that there will be a resurrection and that the soul is immortal. Many intellectuals were losing their religious faith and looking to something else for consolation. William Wordsworth, the great English nature poet, was probably the first poet to turn to Nature for inspiration. He was evidently hoping to find a new source of hope and consolation to replace what he had lost along with his faith in traditional religion. His greatest poem on the subject is "Ode on Intimations of Immortality." Bryant's "Thanatopsis" seems to be directly inspired by Wordsworth--but Wordsworth was an inspiration to Ralph Waldo Emerson and many other poets and philosophers in England and America.
Nature, for Bryant, does not have much consolation to offer to the reader who is experiencing depressing thoughts about death. The best Bryant can say is that it happens to everybody and that Nature will continue to exist in all its wonder and beauty after we are gone.