This theory competes against string theory and loop quantum gravity. In my opinion string theory is a waste of time. It should be noted that it's not just casual set theory which imagines a universe without a beginning - loop quantum gravity does the same. In fact even Georges Lemaitre, who came up with the concept of the Big Bang, thought the Big Bang may not have been the beginning. Lemaitre, who was a Catholic priest, even persuaded the Pope not to say that the Big Bang was confirmation of the Biblical creation story because there was a chance it may not have been the beginning of things.
"A huge part of the casual set philosophy is that the passage of time is something physical." This - right there is why I lean towards casual set theory as being correct according to my intuition.
(HT Newmark's Door)