There is a trend in professional tennis toward an entourage of coaches rather than a single coach. This approach is epitomized by Andy Murray, who has become far more successful after dumping the well-respected Brad Gilbert in 2007 for a team of coaches. I believe the concept of having a single "coach" doesn't actually make much sense in tennis, but has just been passed on from other sports.
The position of coach for a professional tennis player is unusual. Unlike team sports, which require centralized authority to govern the team, tennis coaches don't "call the play" or make any decisions for the player during a match. In fact, "coaching" - defined in the ATP rulebook as "communications of any kind, audible or visible, between a player and a coach" - is prohibited during ATP play. (In reality, general words of encouragement from a coach are tolerated as long the coach does not attempt to impart any technical or tactical wisdom during the match.)
I believe the work of tennis coach primarily includes the following services:
1. Source of confidence and motivation
2. Strategic advisor - both generally and against particular opponents
3. Diagnosing and repairing technical flaws
4. Physical trainer
5. Hitting partner
These tasks are mildly related, but each can easily be outsourced to a specialist. It would be surprising if it were optimal for a single coach to handle all of these tasks.
Confidence and motivation is probably the most important and might best suited to a family member, which might explain why so many successful players have a parent, uncle, girlfriend, brother, etc. as a coach. It would also be confidence-inspiring to have a group of experts advising you.
I have often wondered how valuable a coach actually is as a strategic advisor. On the surface, it would appear to be the primary purpose of a coach and hugely important to observe how the player is actually winning and losing matches and describe the big picture to the player; Andre Agassi claims that Brad Gilbert had a significant positive influence on his game because Brad explained what made him feel uncomfortable when he played Agassi and helped Agassi feel what his opponent feels. (Indeed, a tragic aspect of tennis is that you will never know what it feels like to hit against yourself and experience how heavy your forehand feels or how difficult your serve really is to return)
On the other hand, the best tennis is played by intuition. Your mind keeps track of the points you have won and lost and it usually knows what you need to do to win. Consciously hitting a shot against your instincts in a match is often a mistake. I think conscious strategy is really only effective if it is very simple, like "keep the ball away from Federer's forehand," and a player doesn't need a brilliant tactical coach to come up with such a strategy.
It's probably more important for players to be confident that they have a winning strategy than to actually have one, so it would make sense to use a former great player or noted tactician as the "strategy" coach. Better yet, the player can employ the wisdom of crowds and receive counsel from a strategy committee, which would be more likely to produce the best strategy and inspire its own kind of confidence.
A tour player usually will not make much progress correcting technical flaws. By the time players turn professional, they have had so much court time that the marginal benefit of working on a particular stroke is usually insignificant. A notable exception is Nadal, who has obviously improved his serve and backhand in the last few years. But, I suspect that he has done this with endless hours of practice rather than any tips from Uncle Toni. Players who want to improve a particular stroke should seek out a specialist on the particular stoke (such as Mark Woodforde for volleys), or a group of specialists.
The role of physical trainer is usually already outsourced to a specialist, as it should be. As for hitting partner, there's no reason why players should be wasting their time hitting with their coaches. Players should be hitting with a fellow pro or with a player with a particular style they would like to master (Federer, for instance, has been known to pay the travel expenses of a lefty who hits with a lot of topspin for a hitting partner).
In almost every case, the services provided by a tennis coach would be more reliable if provided by a group of experts. Darren Cahill, Brad Gilbert, and Patrick Macenroe, when speaking as commentators, don't always agree on the approach that the player should take, but when they agree you can be almost certain that they are correct.