That's really interesting, because in the region of the US I came from, I never once saw the cake shared out amongst the guests. I mean, I've been to a lifetime of US weddings.
And I've been to a lifetime of American weddings and I have never been to one where the guests
didn't eat the cake. I think the US is a mish-mash of various traditions.
I've only been to three weddings in the UK but in each of those the cake was a beautifully decorated fruitcake with rock-hard icing, that was cut up and given to the guests in decorative boxes to take home. People were surprised when at the first wedding I took my piece out of the box to try a bite?
Also, at every birthday party my children have attended in the UK (dozens) the birthday cake has never been eaten at the party, but a piece was given to each child in the party-bag at the end, to eat at home.
I'm with the others though, you should definitely do it the way you want at your wedding!