Interesting. I was not aware of that. Here are my thoughts.
First, I would say that I have no answer to your question as to what can be done about it. I think it is a new look that graphic artists are trying to make and so short of changing their minds, I don't know what to do.
I do have some experience in the graphic arts (just enough to make me dangerous). High contrast is important for signs and attention getting headlines. It also makes it easier on us old people who have to use reading glasses to read (high contrast is easier for us to see).
But high contrast can also get old and is an old look. The first website you mentioned is high contrast and to me it looks amateurish (even though it is well done, if not professionally done) and a bit "in your face". I was almost disturbed by the high contrast by the time I reached the end of the website.
In the early days of computers, high contrast was the norm. Light text on dark background (as in the banner ad at the top) was also frequently used. But that was also in the days when computer monitors only showed 16 or 32 different colors/shades. Today, monitors show millions of different colors/shades. Graphic artists take advantage of this by using subtle changes in shade and color (it gives the piece a professional look).
On the other hand, I have come across low contrast that is unreadable (I do not remember any on the internet, but then I usually am wearing my reading glasses when I am on the internet), like menus at some restaurants and certain magazines. With some magazines, I have to get a magnifying glass out to read them and I do not always have one available, so the magazine goes unread (and thrown in the trash). So I would agree with you about the problem of low contrast in these situations, but...I like the low contrast.
I like the low contrast as long as it is readable, but at what point is something unreadable. I think that is dependent on the reader.