The taskbar being available everywhere is the only "absolute" improvement (potential improvement, depending on whether overloading the bottom edge causes problems or not) here though, because the taskbar is a very powerful tool and there was nothing like it available for modern apps (or rather for use across the whole system) before.
All the other stuff (title bar, context menu, etc.) might be welcomed by some/many users for its familiarity and semi-consistency with desktop, and I'm not putting that down - it might be enough to make them the right thing to do. But IMO they're not really inherently any better for the mouse - they just have a different, overall comparable, set of pros and cons.
Take the context menu for example - it has the downside of messing with multiselect. One of the nice things about the original Windows 8 input design is that it did finally introduce a simple, consistent unified model for selection, multiselection and commanding, all done with right-click. Right-click anywhere for global commands, right-click on an object to select it and show its commands (and global commands), right-click on multiple objects to select all of them and show relevant batch commands (and global commands). No need for cruft like double-click or Ctrl-click (that, even after decades, are still confusing to/not understood by a large swath of users). Conceptually a much better model. (There are other advantages of the app bar which I won't get into right now)
Of course as many people have pointed out, the implementation in Windows 8.0/8.1.0 required extra mouse travel from the selected objects to the app bar (and back again), which is definitely a real disadvantage. But I think there are better ways of solving this problem without sacrificing the advantages of the new model. For example, the Office "floatie" toolbar that appears near the cursor when you select text etc. in Office 2007+ seems like it could fit the bill. It's made available directly when the selection changes (no need for separate explicit selection, multiselection and commanding actions), requires little mouse travel, but is designed to be inobtrusive so you can ignore it when not relevant.