Readability is hurt by having body text in different font families, different weights, different sizes, different shades of gray on every other fucking website. Web designer can't choose readable font for me, because readable font is any one font I use the most.
The good thing is that Firefox still has option to override all fonts and use a single one chosen by the user. What is missing though is option to limit font weight to 400 and more.
At the moment I simply don't use websites that use thin fonts. Also websites that abuse fonts to display non-standard (non-unicode) icons fail utterly with user selected font families.
Other than that, having single font family everywhere is much more pleasant.