'Twas a good read. It seemed logical and well-thought out. However, I have some reservations concerning it. First of all, the "grey goo" scenario can easily be extended to humans. If we continue to reproduce, or self-replicate, at our current rate, we could easily destroy all life on earth not related to keeping humans fed. Then, if we leave this earth, we will do the same to other planets, potentially destroying all life not related to keeping us fed.
However, the above scenario discounts the fact that not all humans have a need to have 9-14 children in a clutch. Recently, people in most countries have been having between 1-3 kids, or none at all. If this continues and extends to all countries, human population will actually decline, unless we find a cure for old age and the problem reappears again, in which case perhaps people will decide not to have children at all for the most part.
Now here's the rub, the synthetic grey goo argument assumes that machines are not really alive in the organic sense of the word. They self-replicate without thinking about why they're self-replicating, indicating they're not really sentient. This is rubbish. We're talking about synthetic intelligences. If a synthetic intelligent is truly a logical and sentient being, then it would a) limit its self-replicating, just as humans are currently apparently trying to do, and

find a way to self-replicate and live their lives without over-straining their environment, just as humans are currently trying to do and *might* one day succeed. If they succeed, then these synthetics might not only be able to prevent any other synthetic grey goo from becoming a problem, but defeat any that arise.
This is really my only issue with the ending, this logic that they must kill us to prevent us from launching the grey goo. Every other part of the ending is ok with me for the most part, honestly.