Until we can get the major operating systems to include some of the most popular open-source fonts, we're stuck with web fonts.
If macOS, Windows, Debian, iOS, and Android all came with Roboto, Source Sans, Lato, Merriweather, Raleway, etc. pre-installed, then we could make the case that if we used those fonts instead of non-free ones we would have consistency across all platforms and better performance for our users.
Since I doubt that day will ever come, we instead need to weigh an inconsistent appearance against a poor experience for those on slow connections. Different organizations will choose to prioritize different things, and that's ok.
A significant portion of marketers and designers will always demand pixel perfection for their websites. I'm just glad we're not putting text inside of images any more.