I think the first question, "Why would you want to invoke jQuery on a shadow root?", is effectively the same as the question, "Why would you want to invoke jQuery on document.body?" E.g., you might want to search within a component's Shadow DOM for all elements that match a selector in preparation for some global manipulation. While a component developer could work around this as you suggest (by setting innerHTML), that's just as cumbersome to a jQuery dev as needing to work with <body> specially.
Of more concern are situations in which the dev is invoking code outside their control. Suppose a jQuery widget exists that performs some useful function, and the widget's create() call invokes this.element.html(). That widget (and any other link it) will fail to perform the expected functions on a shadow root, and the code is outside the dev's control. A common case of this might be wanting to wrap a jQuery UI widget as a web component to encapsulate it and puts its contents out of reach of the widget's host. For an example of a jQuery UI widget wrapped in a component, see http://jsfiddle.net/Jan_Miksovsky/y2agp/ (in Google Canary).
The dev is forced to work around the problem by placing a placeholder div (or other element) within their shadow root. The extra layer may not seem bad, but if you have a component-centric app architecture, you could easily end up with many hundreds of components on a page, and the extra div per component adds a lot of clutter.
Your point about the general case of other jQuery functions is well taken. My own framework only needs .html(), but it's reasonable to expect that other people will assume other functions work as well. As it turns out, a quick check shows that .append() does indeed work as expected on a shadow root -- but something like .css() does not, because a shadow root doesn't have a style property. (Although upon reflection, if it has an innerHTML property, there's a case to be made that it should have style too. I'll ask about that.)
I can see that, before tackling this piecemeal, it might be helpful for the jQuery team to review a more complete assessment of what the current and expected behaviors of all jQuery functions are when applied to a Shadow DOM root. If you like, I can take that on, i.e., see what works as expected and what doesn't, compile the results, and submit a recommendation as to where jQuery could fix things. (In some cases, where the current spec doesn't support the expected behavior, the result might be useful feedback to the folks working on the Web Components spec.)
Would that help?