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That's true but there is still no guarantee that it will work out under those conditions. Now I think you are specifically referring to players who played for their club and then also become a coach of that club. The identification level is high, but still it doesn't make a good coach yet. Not every player is born to be a great coach. You can see all kinds of examples and it doesn't always have to be the club they were raised in when they take over the coaching position. Xabi Alonso is doing an incredible job, Steven Gerrard is losing all his credibility. Wayne Rooney is a diificult case in my opinion. I think he really wants to but lacks some charisma or something.
There are no successful Premier League players who have become great coaches, but there are many players who play in a La Liga team who have become successful coaches. Steven Gerrard, Frank Lampard, Wayne Rooney, Vincent Kompany are some of the players who are currently coaches, but all of them are not great coaches. Maybe it's a bit different from players who are former Serie A and La Liga players, some of them are successful coaches who have won many titles so far.
Indeed, there is no guarantee that a former player who coaches his club can bring much success to his club. Pep Guardiola and Luis Erique are two Barcelona coaches who were successful as Barcelona coaches. Carlo Ancelotti and Zinédine Zidane are two successful coaches with Real Madrid, but Ancelotti was also successful with his former team AC Milan.