You could show the same thing by relaxing those assumptions. It would just require a lot more algebra. The key insight is that, holding everything else constant (which is done in the lecture), weakening your accuracy to one side increases the probability you target that side.
I think you need to do the algebra. You can't make a blanket statement like you want to.
You have taken things to an absurd extreme and gotten one result, I can "relax the assumptions" to the opposite extreme and get the opposite result:
Suppose the goalie only blocks 10% of shots when guessing correctly, and the kicker makes 80% to the strong side and 50% to the weak side. In this model it is obviously better to always kick to the strong side.
