1. There’s no reason the UK “has to” go after the carrier. The UK can easily produce more defense than Germany could ever have a chance of attacking per turn until they get Japanese assistance (via bombing) and take Russia (to help them make enough money to build stuff) and they would be perfectly safe leaving the carrier right as it is. But even if they “had to” it would simply be a 1/2 chance of losing one fighter for a very high chance (if they sent all 3 planes) of killing the carrier. Also, the carrier really doesn’t do anything on its own.
2. If you waste your German money on a carrier, you’ll make your opponent happy since that basically hands Germany to a Russian player who doesn’t have some psychiatric condition.
3. A carrier won’t get you the ability to make a land attack, because ships don’t attack land in this game. The carrier could be used to defend German transports being built in theory, but only if Germany either gets the carrier to the Baltic (a questionable idea, and one that would take way too much trouble with it trying to pass the North Sea) or builds the transports in Italy (an even more asinine idea since it basically hands over 2 rounds’ time for the UK to build before they can carry anything over. If Germany builds transports for even one turn they’re essentially handing EE to Russia, and if for 2 turns they’re basically giving up their capital.
And 4. Germany going after the US is even more asinine. Even if Germany could build up transports, it would take them 2 turns to reach the US, in which time the US could easily build from 20-24 infantry units unless they’ve somehow lost more than 6 IPC/turn income (which, in my opinion, should be impossible). Even if that’s all that’s on the US - 20 infantry - to even get 20 infantry to attack the US would take 10 transports + 20 men (a cost of 140 IPCs). Last time I checked Germany has no way to do this. And that’s to have a DISadvantaged attack.
I would love to see a typical scenario you consider a possibility for using a German carrier to help invade the UK. Please provide one, maybe builds for a few turns, what you’re doing to defend against Russia, and what a final attack might look like, and most importantly - what you do with the carrier?