Think of Arsenal, for a moment. Is that a club you would consider signing for as a player with aspirations of winning a major trophy?
Pretty much everyone says "No" to that right?
Not sure how many seasons they've not qualified for the CL since the turn of the century, but it can't be many. So why would we not sign for them (as players)?
Because they've won nothing for 7 going on 8 seasons, and don't look like winning anything soon. They're losers. They're a selling club. You're better off with Spurs, because they look like they MIGHT win something (unless their manager leaves).
A cup double this season would show we still have the METTLE to win things. It suggests that even if we miss a CL spot it won't be long before we're back there. In short, Liverpool's stock is rising. It won't rise as much if we get 6th and 2 cups vs 4th and one, but 4th and no cups would look just like Arsenal has since the Invincibles broke up. No recent success. We'd get more money, but it's not enough by itself.
The cups are vital to our progression because they raise the profile of the club; we can't be bad if we win stuff, no matter how apparently insignificant compared with the Champions' League title. How many English clubs have won the CL since 2000? Just 2? Only once each? One of which was Liverpool? The CL group stage does bring a lot of money to the club, and does enchant the top end of the player scale, but these are players we couldn't even afford to pay weekly.
We need these cups. We need 4th as well, because of all the things it brings (mainly business and exposure), but one can lead to the other. 4th is vital to our progression as a club in this age of the power of money in football, but *success* is not something easily bought and then sustained. Success breeds success. Winning the Carling Cup might not do much for the club's bottom line or in the hearts of some of our fans, but those players will take pride in lifting the trophy, and that will surely make them stronger for the experience. This kind of team building is exactly what we need - an experience that pulls everyone together, has everyone playing for each other. Without that we're just a worse Arsenal, and no one with aspirations will want to play for such a club.