Most "arguments" are either wrong in some way, apply only under rather specific situations or are about the interests of the owner, not the rabbit.
No, the manure doesn't get "hot", hay mixed with thir poop goes straight into my vegetable garden.
No, they don't starve on hay, that is nonesense. Malnutrition - well, it depends. Hays can differ a lot in nutrational value, that might be something to consider when you by your hay directly from the farmer like I do.
Personally I do think a rather diverse diet - with hay as the staple food - is preferable.
Yellow feet? So what, the owners vanity is of no use to the rabbit.
Mites? Nope. More likely carried in by living things.
Mold can be an issue with most feeds.
Messy - well, he's got a point there, but that depends mostly on your setup, but again, this does not bother the rabbit in any way - I know.
There are several good ways to feed rabbits, not just one, you can do it right several ways depending on your resources. You can definitly feed a rabbit without hay - mine don't eat close to none through summer when fresh forage is available - hay is just the conserved form of that forage.