Well for one, castaways are humans and we know humans exist because they can be observed. Quite a leap to go from "evidence of a human on an island" to "evidence of an invisible anthropomorphic immortal sugar daddy who created the universe." BTW, your claim that the universe *looks* like a universe that a god created is entirely subjective.
So the analogy is unfair because it grants a scenario where an intelligent agent is at least allowed as
remotely possible? even though the deserted island is explicitly, actively guarded against this? so ID must be ruled out entirely to allow chance to win out by luck eventually? Yes I know- that's the problem. The same is not true in reverse, a theist does not need to banish natural mechanisms to allow God infinite tries!
And we know of no such security force preventing intelligent creation of universes, nor do we know of any spontaneous universe creating device which the analogy grants you 100%
So the analogy is actually very heavily biased towards a naturalistic explanation, yet you still choose ID- simply remove the distasteful concept of God, and we agree on the best power of explanation do we not?
Natural processes (evolution) explain the diversity and complexity of life just fine,
classical physics explained all physical reality just fine too, so much so it was 'immutable'- at a similarly superficial level- but explaining life, including it's capacity for adaptation, using that very same capacity.... is like trying to explain gravity with classical physics, doomed to paradoxical failure
which was a far bigger problem for atheism prior to Darwin than current gaps in cosmology are for atheism today. If you view God as responsible for things science has yet to explain, then your god is an ever-receding gap in knowledge that continues to be filled in by new discoveries.
On the contrary, ID objectively explains the rocks on the beach just fine, just as it always did the origination of the novel information required for the universe, even before atheists finally conceded that the universe DID begin in a creation event. An infinite probability machine (multiverse) was
always the last gap to retreat to, after static, eternal, steady state, big crunch etc were all emphatically debunked