You're well ahead of me in the math department, and intuition isn't worth much unless it's well-informed. For what it's worth, I like the oscillating universe because it avoids the problem of the universe's being strictly a one-time affair. That definitely is counter-intuitive.
Not necessarily counter intuitive. If you consider what intuition is, or could be. I think it those thoughts and ideas that cannot be clearly expressed in language which is based upon all our past knowledge and experiences. It is those math ideas, for example, or ideas about an oscillating universe that cannot be formally expressed yet you know intuitively, are true.
If you consider the survival of the fittest, the universe that survives is the universe that is self-perpetuating. Thus a universe that is a one-time affair might be doomed for self-destruction.
Life itself can be viewed as innately oscillating if you consider yin and yang, positive-negative charges, magnetism, binary zero sum, plus minus instances...and nature abhoring a vacuum so that it is constantly in flux and thus perpetuating life. (OK, time for a nap... ;))