Seems worth adding since it looks like browsers aren’t doing a great job at it (looks like Safari on iOS always uses blue no matter what the background color is?).
If we do caret-color: currentColor; it would match the text color of the input, which would also make things easier.
Edit… now that I think about it for a minute, this would make the caret a little less obvious on iOS because it would be black and not blue (for the default theme anyway). Maybe we should only set it on dark themes… 