There's no doubt new equipment manager Kevin Kierst is wild about the high numbers, his reign as equipment manager also saw 60s assignments to Jon Rauch (60), Jack Egbert (61), Elvin Ramirez (62) and Josh Stinson (64); and a 73 issued this year to Robert Carson. These jerseys at one time were almost exclusively a spring-training thing, with the only exceptions being brief debut appearances of 61 (Jesse Orosco, Mario Ramirez) and 62 (Hubie Brooks) in 1979 and 1980.
The Mets then went more than 20 years without issuing a 60s jersey until Jeff Duncan came along in 2003. Chan-Ho Park and Livan Hernandez both later wore 61, but came to the Mets having worn that number elsewhere. Scott Schoeneweis broke 60's cherry in 2007 but was also continuing a tradition. So perhaps then the spritual grandfather of today's common Met-relief-pitcher-in-the-60s is good old Elmer Dessens, who debuted 64 in 2009.
We have yet to see a 65, 67, 68, 69, 70, 71, or 72, but there's still time.