OK, this has been bugging me for a little while.
You’ve got the Americas Cup, the World Cup, the Stanley Cup, the Rider Cup, all these trophies that loog like a giant goblet or a punchbowl on a pedestal. But Why a cup? Why not a plate or a spoon?
Many years ago did strapping warriors in a long forgotten kingdom arm-wrestle for a coffee mug? Does it relate back to the knights of the round table searching for the Holy Grail? Why a cup?
I’m sure there is a direct connection to the fact that early awards were for atheletic prowess. What better thing to offer a triumphant contestant than a cup of wine to slake the thirst resulting from their exertions?
From there it is only a short hop to the heavily embellished lovers cups that have become the standard issue for such prizes.
With all those cups mentioned in the first post, one could only add “C-cup, D-cup.” Talk about your trophies. 
Seriously, the word “trophy” only comes into English in the 1500’s. No mention that it might have to do with cups. So I would rule out the ancient Greek connection. While I realize this may be a leap, I don’t really care*
*Using the Handy rule.
That makes sense to give everyone a drink after the race and let the winner keep the cup, jug, ampulla, whatever.