Do you think Jerry played out the Garrett decision to the bitter end for public attention ?
No, Jerry's mind had to process both Jason's family ties to the organization combined with his own infamous hand selection as OC before selecting HC Wade laid the groundwork for what would be that long tenured relationship. All the embarrassing interviews by Jerry and the coach in training and equally disappointing coach speak by Jason when he would often say "Jerry makes those decisions." If Jason could have accepted a front office title position Jerry would have sent him upstairs in a heart beat. So in a small clash of egos I'm sure Garrett is hoping to prove his legitimacy with the Giants. The Maras/Tischs knew him when he was with the team before so the relationship there had been previously established.
Short answer to your question though is the Garrett to Jones family dynamic came into play and Jerry just wanted to save public opinion face that one of his adopted family projects didn't quite work out.
Remember the Jimmy and Jerry facade. A mutual agreement of 2 egos.
Well Garrett is tremendously more humble than Johnson by nature but he is still a man with a certain level.of pride who I'm sure will be out to prove his own meritocracy as a coach.
Apologies for butting in unannounced and doing my whole behavioral counseling diatribe on you as that is my background.