I am pretty positive your card information won't get send, that's not how it works, skimming works differently than you think.
If my card gets compromised including skimming I won't lose anything, it's the bank loss, that's how it should be anywhere in this world, think this is not the case in the states though.
As your "there’s the added convenience of not needing to pull out anything out of your pockets' statement, that's just plain silly, I have my card out in no time, before the cashier even asks for it.
Lower your arm, get hand into pocket, open your wallet or wherever it is in, voila, simple hey.
People nowadays.....
Me too, and my cards are in my phone case.