Why is Buddha needed?
In Buddhism, rebirth will occur endlessly without the attainment of Nibbana (which does not happen naturally or by some sort of evolution). There is no automatic nibbana. Natural spiritual evolution is a Hindu idea (see Chapter 26 of Autobiography of a Yogi by Paramahansa Yogananda) and not a Buddhist one. 

In Buddhism, all beings are not naturally progressing towards Nibbana. It is possible to be reborn as a Brahma, then later as a pig as in Dhammapada 338-343:


  On one occasion, while the Buddha was on an alms-round at Rajagaha, he
  saw a young dirty sow and smiled. When asked by the Venerable Ananda,
  the Buddha replied, "Ananda, this young sow was a hen during the time
  of Kakusandha Buddha. As she was then staying near a refectory in a
  monastery she used to hear the recitation of the sacred text and the
  discourses on the Dhamma. When she died she was reborn as a princess.
  On one occasion, while going to the latrine, the princess noticed the
  maggots and she became mindful of the loathsomeness of the body, etc.
  When she died she was reborn in the Brahma realm as a puthujjana
  brahma but later due to some evil kamma, she was reborn as a sow.
  Ananda! Look, on account of good and evil kamma there is no end of the
  round of existences."


The Self disappears and arises again endlessly through rebirths - which is explained through dependent origination. As stated in Milindapanha 3.5.5, rebirth is like light of a candle passed from one candle to another. It can be passed on forever. Also see this answer.

It is indeed possible to become enlightened (i.e. attain Nibbana) without ever encountering the teachings of a Sammasambuddha.

Such beings are called Pacceka Buddha or Pratyeka Buddha (see here and here), which literally means "private Buddha" or "lone Buddha". You can find some details in this question. A Pacceka Buddha would not have the ability to teach others and start a Buddha Śāsana.

While it is possible for someone to become free from suffering this way, it is immensely harder than if someone learns it from a Sammasambuddha (or Samyaksambuddha).

My analogy here is that Albert Einstein is a "Buddha" of physics who discovered the Theory of General Relativity and taught it to others through his groundbreaking published paper and his lectures to trained physicists. While it is possible for others to discover this on their own, it is immensely difficult. It is easier to learn it from Einstein and from those who have learned it from him.