Great work @crokkon! I agree with your analysis.

On the last point:

This means that using Math.sqrt() may give results that are up to around 6% off the values that are calculated by steem. This is however not necessarily the resulting error on the final curation reward in STEEM. This value had to be calculated with proper error propagation on the full formula.
I compared the results with both functions for a handful of posts manually and saw deviations in the order of 0-3%, but this is obviously not statistically significant.

I think that the impact on curation rewards of the simplification can be quite significant. The formula for curation rewards depends on generating a small number as the difference between two large numbers:

curation weight =
sqrt(prev_rshares + vote_rshares) - sqrt(prev_rshares)

The impact from using the simplified square root will be different for the first term and the second term in the above calculation, and both terms are large. As an extreme example the impact could be 6% of sqrt(prev_rshares + vote_rshares) and 0% of sqrt(prev_rshares). This would translate through as an impact of 6% of sqrt(prev_rshares + vote_rshares) on the curation weight. This will be much more than 6% of the curation weight because the curation weight is a smaller number.