We're often told that if there is one fatal flaw in Rex's coaching philosophy, it's that he is loyal to a fault and most will point to his continued usage of Mark Sanchez as evidence--at least until his latest meltdown in Tennessee. His personal draft picks, like John Conner, have been held against him in the past and will undoubtedly continue to be subjected to discussion moving forward.
However, he has largely been the driving force behind the Jets' defensive selections which have included Muhammad Wilkerson and Quinton Coples and others such as Kyle Wilson, Antonio Allen, Kenrick Ellis and Demario Davis. His initial comments on Stephen Hill indicated he was not at all thrilled with drafting him in the second round (which based on his rookie year, they definitely could have waited to snatch him up) and under his watch emerging players such as Jeremy Kerley and Bilal Powell have been drafted.
The extent of his influence can only be speculated on but it's a near certain fact that Rex had some input in the Jets drafting some of their top defensive players while their offensive strategy has largely been hit or miss. This may be more of a reflection of the scouting department and the Bradway/Tannenbaum tandem than Rex himself as the Jets have struggled to draft offensive talent dating back to 2002 and probably even farther.
Since 2002 the Jets have drafted: TE Chris Baker, G/C Jonathan Goodwin, FB B.J. Askew, QB Brooks Bollinger, G Dave Yovanovits, WR Cotchery, T Adrian Jones, G Marko Cavka, RB Derrick Ward, RB Cedric Houston, TE Joel Dreessen, WR Harry Williams, T Ferguson, C Mangold, QB Kellen Clemens, WR Brad Smith, RB Leon Washington, TE Jason Pociask, G Jacob Bender, WR Chansi Stuckey, TE Dustin Keller, QB Erik Ainge, WR Marcus Henry, G Nate Garner, QB Sanchez, RB Greene, G Slauson, G Ducasse, RB Joe McKnight, FB John Conner, RB Bilal Powell, WR Jeremy Kerley, QB Greg McElroy, WR Scotty McKnight, WR Stephen Hill, RB Terrance Ganaway, T Robert Griffin and WR Jordan White.
Of that list, Goodwin has found second wind success with the Saints and currently the 49ers, Ferguson and Mangold are two staples on the Jets' offensive line, Kerley emerged as a rising receiver this past season while Powell showed marked improvement and potential. Leon Washington is mainly in a reserve role in Seattle but earned his second Pro Bowl appearance this year based on his special teams abilities and then of course there's Cotchery who was a consistent part of the team until riding the pine in Pittsburgh for the majority of the last two years while the tenures of Keller, Sanchez, and Greene have been inconsistent and disappointing.
So of the 30 some odd players listed, only a handful have made a meaningful impact in the league whether it was with the Jets or elsewhere while a few others, such as Hill and White, are still early in their careers. To me that indicates the problem goes well beyond Rex and placing the entire blame on him is lazily ignoring their missteps well before his time that could have netted them more talent than they currently have. That isn't to say that it absolves the Ryan administration of their sins but, it's also unfair to blame his tendencies to go defense when two other coaches in Herm Edwards (DB coach) and Eric Mangini (offensive assistant, DB coach, D.C.), under Bradway/Tannenbaum then Tannenbaum/Bradway, struggled too.
All of that being said, I think Rex's opinion should warrant consideration by the new general manager but not be taken as gospel either. The Jets need to establish that line of communication because that's how successful teams are built but, they also need to be smart and keep Rex in check so that way there's a balance of sorts that will hopefully yield better results.