The name of the template tag is misleading, I agree: It separates the shadow DOM elements, the "template", from the light ones, the children slots.
Different server-side instances of the same components won't necessarily render the same shadow tree, so client-side reuse was out of the question for declarative shadow DOM. But unlike client-side template, you get to paint components much sooner, during the parser, or even without JS enabled.
As for why a shadow root instead of the markup directly, well, that's kinda like asking why use web components at all, which I thought was part of the premise of this reply chain.
Even without JS, the shadow DOM gives you scoped CSS and isolates the shadow elements from outer DOM and CSS selectors. And custom elements, the other half of web components, can be used in HTML before defining them in JS, at which point you get to enhance the entire page at once, so now you can progressively enhance properly isolated components possibly written with different frameworks.