This is on track to become a "built-in feature of ASP.NET Core 3.0" – recall that ".NET Core" runs on Linux, etc.
Much C# development is still for internal business applications. For these applications, the overhead of shipping the .NET runtime to the browser in WASM - which https://blazor.net/ sadly does not seem to mention - may not be a big deal, especially if they can be cached with service workers.
Keeping engineers fungible and cheap to hire & train is a priority for enterprise software divisions. Software ecosystems that rely on the patience and curiosity of developers to explore an uncoordinated constellation of packages and design their own architecture (eg; Java, React ecosystems) can be suboptimal.
.NET's historical "all batteries included, all applications the same" promise has been key here. But for rich frontends, Angular (their current choice) has, ah, high training costs.
If Blazor works well, .NET Core may become the first truly full-stack, integrated, get-it-all-here, framework for modern web app development.
As an uninvested bystander to enterprise software development, I'm curious to see how this goes.