Good article, and important. To add, some of what I am going to write below is the result of recent readability studies.
Very often the problem is not black text. Black text can be GOOD for small thin fonts such as for body text (i.e. less than 21px and 400 weight etc).
It is true that excess contrast for large and bold type like headlines can cause problems for some, but the more significant issue usually relates to the total page luminance.
The real problem? A background that is too bright. #fff is too light (though there is a dependency on the eye's light adaptation state)., Even the #ebebeb used on this page is a tad bright, I personally try to keep BGs under Y80 which is #e8e8e8 . #ccc or #ddd is much more comfortable to view.. Adding a beige tone by reducing the blue channel is also helpful, such as #EDA, in part because blue is a major cause of glare.
For body text, contrast should be over 10:1. The WCAG_2 spec is a bare minimum, and not enough in many cases — the future WCAG_3 contrast using APCA™ will be more comprehensive this way. Big bold headlines though can and often should be much less.
W3 AGWG Invited Expert
WCAG 3 co-author (contrast)
Myndex™ Perception Research