It's already at a stage where League Cup worthless, there is no prestige in winning it.
The FA Cup is a tough one for me to swallow (and an impossibility literally), I adore it but every year it's star burns less and less bright. Oddly it's history that keeps a flicker of life burning, but the FA does need to just bite the bullet and makes this Cup worth winning again, they have to whack a £30m winners prize fund on it. That sounds crude but there is a reason why Wimbledon has remained relevant and it's because they haven't ignored the $$$$.
The main point area I would disagree with you on, although not strongly, is that the nature of a knockout competition is that you can still draw some absolute dross. City's first win under the new regime was against Stoke (they famously lost to Wigan so it's not always a given), Woolich's first trophy in 15yrs was against relegated Hull, then followed up the following year against relegated Villa.
If you are good enough to be competing at the pointy end of the table and latter stages of CL the domestics will present themselves to you. In our recent adventures, we draw the champions in all bar one if I'm not mistaken. We need to be present at the top of the table consistently and we too will get our final against Wigan.
(Reaches for coat)