A lot of high contrast combinations are less accessible and even if it doesn't make the text illegible, too much contrast is going to be a strain on the eyes for most people.
Generally, WCAG AA or AAA is enough for most people and you hit that already with #555 on a white background. Something like #1a1a1a is close to the darkest I'd use in most cases.
Why wouldn't people who need less contrast simply reduce the contrast on their monitors, though?
It seems to me as though designing for those who need low contrast excludes those who need high contrast, but not the other way around.
From your link:
> The solution for contrast sensitivity
> If you feel that your child may be suffering from this issue, the first thing to do is test some tinted acetate sheets placed over the page of text.
Because I don't want to make everything else look worse just to lower contrast in text?
And support for low contrast doesn't mean excluding others, it can just be a setting. Like Windows has been doing for a long time with its high-contrast mode. Websites and apps are increasingly adopting dark themes, next we should push for a switch between high and lower contrast. It's just as easy from a technical standpoint. Browsers are already pretty far, letting the user set specific fonts and font sizes, and Firefox' reader mode and its options are great as well.
If a site provides a widget where contrast can be beefed up, probably part of the dark-mode / light-mode widget, that seems OK.