It can’t be integrated into the browser, because that would be a bit of proprietary technology (use this browser! supported on this device!) that would horrify the modern web development community. And extensions are just another name for plugins — we had it with Silverlight and Flash, it worked for plenty of people, but it runs into security issues, permission issues (corporate users need to be allowed to install the plugin), compatibility issues, etc.

That said, you are correct that large parts of the Blazor runtime are common to all Blazor applications. Ultimately, they will be served from a CDN in a way that will allow the browser to cache them. So most of the time you should only pay the cost of downloading the full framework for the first Blazor app you visit, and get a smaller download for other Blazor sites (with certain caveats).