As I see it, there are two possible explanations for a fine-tuned universe:
an insane amount of luck (or something other than luck, such as a supernatural force)
multiverse
The argument for multiverse is precisely that it does not require the insane amount of luck.
Your argument is that with the insane amount of luck, the multiverse is not necessary.
That is correct, but then we are back to the original question: why did we get so extremely lucky?
It is fascinating to see that the official science has finally discovered what Yudkowsky wrote about a decade ago. Better late than never, I guess.