And is a prime example of how mercenary and money grabbingly shameless the league and football in general has become, detached from the fan and sucking up to anyone with money. It should just be the LEAGUE CUP, with the champions of it going into the Champions League, the FA Cup should just be the FA Cup not the Emirates or whatever cup it will be, again, the champions of that should go in the Champions League, and the Premier League should just be the premier league with the Champions going into the late stages of the Champions League. Its all about fucking money, nothing to do with football. Messi, Ronaldo etc, would still be playing for the big teams, whether they went for 10 million or a 100 million - all this money swilling around just inflates prices, but as it is transfers are going to always be gobsmackingly tedious and money centric. The way its going the European Super League, made up of the top 3 or 4 super sides around each country in Europe will be the main event and nobody will give a fuck about every other team, "inferior" leagues, down to grass roots. Carabao? My arse. Good morning.
You have two different issues here, 1) Which European competition you should qualify for having won a cup and 2) The principle of sponsorship in Football (but name me any other sport that does not rely on sponsorship)
To you first issue I would say to win a cup you need to win 8 matches, many of them possibly against lower league sides, to qualify for CL in the current format you have to be consistently better than almost every other club in the league (for automatic qualification) those teams only should go to compete with Europes top teams.
To your second issue, what difference does it really make to you whether it's called The League Cup (which many of us refer to it as regardless of who sponsors it) The Milk Cup, The Littlewoods Cup , The Caraboa Cup or anything else ? I don't agree that the game has become detached from the fans with sponsorship, on the contrary, sponsorship has enabled clubs to reduce ticket prices in many cases, even down to grass roots football and Sunday league clubs are dependant on sponsorship whether from the local builder or the butcher they need the money for kit, pitch hire etc.
Just call it the league cup and the FA Cup, most people do.