Websites can't really assume
anything that's not a web standard. If this is important to them, they should be lobbying the web standards bodies to come up with a list of fonts that browsers are required to make available. Then the browsers will pull them in as dependencies when they're installed.
The Linux distributions did their jobs with excellence. The fonts are all there and installing them is a oneliner. The web folks made their own OS though so if anyone is to be blamed it's whoever is in charge of that OS called the web platform.
Who's in charge of the web as a platform these days? Google. Who is no doubt profiting from the Google Fonts thing.