Here's what I'd tell them....
Kids have lots of stuff memorized.
--Lines from movies
--Sports team rosters, or favorite player's numbers.
God's Word is at least as important.
I might even play a 'game' of asking the kids to demonstrate things they have memorized from that list.
The question is not should they memorize verses, but how we can do it in such a way as to make them happy to do it!
BTW: This very subject is one of the big reasons I took computers seriously in the 90's as TEACHING tools. The kids would eagerly work on memorizing verses on the computer, but otherwise turn their noses up to that same verse on paper!