Clearly, aesthetics are important but aren't the ultimate goal of design. And often poor readability doesn't get noticed during the design process, as we are not like our users. We don't read the texts as a visitor does.
W3C's Web Content Accessibility Guidelines set the minimum contrast between text and its background so that it can be read by people with moderately low vision (which is quite common).
A readability experiment conducted on web pages shows the importance of sufficient contrast between the text and the background.
Another experiment confirms that reading time is lower when there's high contrast between the text and the background. What's more, contrast sensitivity declines with age. Also, see more papers on readability.
Connie Birdsall from Lippincott says that "Ensuring print legibility presents a creative challenge to the design community and prompts us to re-examine what we do. It also reminds us to keep audience needs top of mind when we design."
Usability expert Jakob Nielsen has shown many, many times that reading on the computer screen is harder than reading printed material even without making the font illegible. And mobile is worse.
.. and many have written about why gray text is a crime here and here...
