The bolded part is an assertion without evidence, unless you can demonstrate former NFL players succeed at higher rates than people who did not play.
Among the final 8 coaches in the NFL playoffs this year. 1) McVay - no nfl playing experience 2) Zac Taylor - No NFL games played. 3) Andy Reid - No NFL playing experience. 4) Kyle Shanahan - No NFL playing experience. 5) Matt Lafleur no NFL playing experience. 6)Sean McDermott - No NFL Experience. 7) Mike Vrabel, extensive NFL experience 8 ) Bruce Arians - No NFL playing experience. for this small sample set, 7/8, 87.5% have no NFL playing Experience. Ron Riveria, Brian Flores.
Based on the the strange theory that NFL teams want to win, there is not really much evidence that former players put teams in a better position to do that as head coaches.