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Isn't that last point true for all substances? That's just how phase changes work.

It's true for first-order phase transitions but not for second-order phase transitions. The article actually talks about it further down:

> the Mpemba effect could happen through a related mechanism that Raz has previously described with Lu in systems that undergo a second-order phase transition, meaning that their solid and liquid forms can’t coexist at the same temperature. Water is not such a system (it has first-order phase transitions),

It would be pretty wild if they were immediate! But.. if you keep it moving at say -1, will it still eventually freeze? I struggle to imagine but don't know why really. Maybe it means something like that. Not that I know why that would be unique to water either.

Water isn't strange. It's state changing is what's interesting. That's where the most energy is converted. From latent hidden energy instead of specific heat.

This is where BTUs come in handy..

But it doesn't seem to discuss the possible effect on speed of freezing.