When Shadow DOM was first considered for use in the client `<link
rel="stylesheet">` was not widely supported as a way to load external styles into
shadow roots. This was resolved in the spec in https://github.com/whatwg/html/pull/1572
and has now long been supported by all browsers.

Using `<link>` simplifies the code and also avoids a possible problem with sites
that have a strict CSP policy that disallows inline styles. In the
browser extension context a `<link>` can still work in that scenario as long as the
stylesheet is loaded from a `chrome-extension://` URL.