I would love this as well, in fact I see no reason why they couldn't have both solo and mute buttons on the flyout. It seems like the decent thing to do given that the flyout doesn't always "fly out" to the same side each time. This inconsistency is what makes it hide the buttons - it's fine when it flies out to the right but hides them when it flies out to the left.
I can imagine that it might not be a trivial implementation from a coding point of view, because it may be the case that the Quadcurve code doesn't have ready access to the track controls.