It translates easier sometimes because tennis is an individual sport, but for the most part you are spot on.
A great player doesn't necessarily make a great coach. Don't think Jordan or Kobe, whose games relied more on individuality, would be suited as great coaches. I think LeBron could make a decent coach since he's always been more of a passer/field captain than a 1v1 dominate player.
In futbol, how many all time great players became great coaches?
It all depends on what type of player that person was. It doesn't necessarily mean they'll be a great coach, but it helps.
In hindsight, one wonders whether Edberg forcing Fred to go to the net so much was really the answer, when Fred has done just fine with Ljubicic playing more of a refined baseline-hybrid game than the game he employed under Edberg. I think Fed played Djokovic better in 2019 under Ljubicic than he did under Edberg in 14-15 when he was s&v'ing a hefty bit of the time. There's other variables to consider, in that Novak also isn't the same player he was in 14-15 (his serve is way better now IMO), or that Fred was switching to a new racquet, so ending points quicker helped ease his transition to new racquet and now the version we see under Ljubicic is just refined.