Well you admit to Bad Play on the part of U.K. so the case is closed. Regardless of what had to go right for the Germans.
And no, resources don’t HAVE to be built to deal with the Japanese Navy, but the reality is 100% of the USA’s income is going into the atlantic, thereby relieving NO pressure on Germany.
A Jap navy with transports off the east coast of the U.S. or threatening australia however, would divert that 100%. Sending a useless navy to South America was a poor decision in this game. Hinsight or not.