Fair enough. In this case, I guess it's a tradeoff between code organization (should the child component be concerned with its position in the parent) versus avoiding rerenders.
The rationale behind that is avoiding re-renders, which can (but doesn't always) improve performance (shouldComponentUpdate can be slower than simply always re-rendering, per a React core developer): https://news.ycombinator.com/item?id=14418576
This is a textbook case of premature optimization. Why make your code harder to read just to achieve some performance gains that likely aren't even noticeable?
Lastly, regarding the ESLint rule, sophiebits put it better than I can:
I don’t recall ever having seen a credible-looking study about this, including in 2015.