The fundamental problem with the experiences of those who have come back from the dead is just that, they came back. They did not die and stay dead, which is important because their experience of death is limited to the time immediately after death.
Hieromonk Seraphim (Rose), in his book The Soul after Death, carefully and definitively shows how almost all of these stories we have heard of “near-death experiences” do fit into a true, full, and traditional Christian understanding of the soul after death, though not always how we might have imagined. If you want to understand more fully (than I have space to write here) how the accounts of Christians and non-Christians, heavenly and hellish, angelic and pagan-god-filled experiences could all confirm one truth, you would have to read his book…and I highly recommend it.
Here, however, I will mention one small point of the Christian teaching which will highlight why we need more than just experiences of immediately-after-death experiences: demons deceive, we know that, and especially when “Satan transforms himself into an angel of light”, we can be assured that we may not be experiencing what we think we are experiencing. Seeing a light or feeling peace may not be such a good sign.
The experiences I will share, taken from the lives of saints or passed down to us by the saints, always challenge us, spiritually. They always bear good fruit. Instead of the pride of getting to see heaven, they bring forth humility. Instead of confirming that I am living my life just fine, they bring about repentance. We will know the experiences we should pay attention to by the fruit they bring forth in our hearts.