I tend to agree that the moon and sun size is not a profound argument, although the comparison with other planets is not really apples to apples. After all, the moon and the sun are the only two bodies which appear to revolve around the Earth daily and on split shifts, as it were, so that their apparent sameness of size is of a different order of coincidence than if saturn and Jupiter appeared the same size. After all, many stars appear the same size, but no one has claimed that as a coincidence, because there are so many stars and they don't have so much else in apparent common as the Sun and Moon.
It's one thing to belittle the moon/sun coincidence, but if their similarity is taken as symbolic of the general, overall cosmological fine tuning, you are faced with a more difficult set if issues, and the coincidence response becomes more tenuous. If you propose the evolutionary model as the explanation, arguing "of course we observe fine tuned parameters, we could not observe them if they were not present" - that will only take you so far.
The reason the many-worlds or multiverse has to be posited is because for the evolutionary explanation requires that selection has something to work on. If there was only one universe, and it just happened to support life, where the billions of other possible combinations of parameters would arguably not have supported any life, then it would indeed be astonishing good fortune for the universe to just have been that lucky strike. Only with an endless succession or number of parallel universes does the coincidence or selection bias explanation become plausible.
Finally, while the banana video is indeed funny, I tend to find this one a bit more in line with my comedic palette.
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