Why would John Dean care about protecting JFK's reputation? Why not keep the stuff and just let Ted Kennedy know that you know...
IIRC, Nixon and JFK got along very well personally even though they were political rivals. Moreover, back in the early 70's JFK was still a national icon, it would have been suicide for anybody to diminish JFK's reputation. After Chappaquiddick, Nixon knew that Teddy's hopes of ever being POTUS were gone, but Nixon also knew that the reason Teddy got off so easily after Chappaquiddick was because of public sympathy over JFK and RFK.