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The whole basis of that scheme was the different relative exchange rates in the muggle and wizard world. There are I think 17 silver sickles to 1 gold galleon, but I'm the muggle world gold is more like 50 times the value of silver. The plan was to take a galleon to the muggle world, melt them down and sell the gold, use the proceeds to buy silver, bring that silver back to the wizard world and have it minted into 50 sickles, and trade those sickles for about 3 galleons.
Like many scenes in HPMOR the author is mostly just roasting Rowling for lazy world building. He didn't have to build a world where everyone else was stupid, the point is that Rowling's wizarding world already fulfilled that requirement.
Exploiting the difference in value of a commodity between communities is a valid way to make a living, traders have existed for a very long time, though if there's little effort required the values will quickly align with each other. Turning it into an infinite money glitch by having a mint convert your raw material into coins is nonsense.
That's all still assuming the coins are made of pure gold/silver for some reason. And assuming the mint is willing to just make money for you in spite what I've already said.
Edit: And that's all if you ignore the fact alchemy, conjuration, and transfiguration exist in that universe so the entire thing is moot anyway. The angle they should have taken is that physical currency makes no sense in a world where you can just summon more, but I suppose that's harder to turn into "I'm so much smarter than the entire world".
I mean if you actually read it, basically every point you made except transfiguration is addressed in the conversation Harry has with a goblin at Gringott's. And transfiguration is addressed later in the book, it's actually a really crucial plot point. Long story short, no, you can't just summon more without the philosopher's stone, which is exceedingly rare.
The angle taken, that from currency to time turners the setting is poorly constructed, is valid. Incidentally, HPMOR Harry suffers due to his "I'm so much smarter than everyone" hubris multiple times throughout the story. Once the story really gets going, Yudkowsky doesn't really shy away from pointing out when Harry's absolutist rationalism comes across as childish, impractical, or straight up unethical.