I think Singles Tennis has no place in The Olympics. The Olympics are primarily a competition among athletes/players representing their nations. Even hardly known sports are given a place in Olympics because they are a celebration of sports and also are meant to encourage sportsmen/women in all sports all over the world. Many great sportsmen in less lucrative sports, in terms of ability, are badly in need of recognition. There are numerous Olympic gold medalists who are unemployed. Most don't get to play their sport professionally as a career.
Tennis is more like Golf/Formula1/Nascar/Pool/Billiards/Poker/Snooker/Squash etc. If you are accomplished in these sports then you don't need the Olympics. Ussain Bolt and Michael Phelps may be rich today but they First Had to win an Olympic gold to get rich. Otherwise they'd be nobodies. Why do players like Federer, Murray, Djokovic, Nadal need Olympic medals? They already have all the money and glory in the world. If you want to make your country proud, go win the Davis cup. It is hypocritical to skip the Davis cup and enter the Olympics. In effect it means that a player is doing it primarily for fame. But why do the wealthy and the famous need fame? No one outside ATP top twenty is going to win an Olympic medal anyway.
As to what The Olympics means in Tennis. Nothing. An Olympic medal is not worth the metal it is made from in Tennis. If you can win a singles Olympic medal in Tennis, you can surely win an ATP1000. If you want to make your nation proud, help it win the Davis cup. In fact, keeping Tennis out of the Olympics increases the profile of Davis Cup which badly needs it. What's more. Established players can happily let the less accomplished players share some fame and honor in the Davis Cup. I don't remember the men's Olympic medalists but I remember Marcelo Rios, David Nalbandian, Mark Phllippousis, Marco Baghdatis etc. If you have talent, the tour lets you make a living. You don't need Olympics. If you are outside the top 200 and Pro Tennis isn't enough to make a living? Then make a living Marcus Willis style. Teaching tennis to casual players, futures players, university players etc. pays more money than what most Olympic gold medalists, forget Bronze Medalists, make after they go back to their jobs at home. In many countries, they work themselves to death. Some die in penury.
Team sports are a slightly different deal. The very fact that it's a team sport means that players share credit. So there is some justification for them in Olympics but even there there, sports with less lucrative pro circuits should get the preference. Volleyball, water polo, field hockey etc. Building a soccer stadium or 50 tennis courts with ball boys and girls costs the host nation serious money. Money that can be used for Anti Doping tests.
That brings me to the only justifiable reason why singles tennis might have a place in Olympics. The Stars bring money to the host nation and the Olympics itself. Fair enough. But then, does signing 100 autographs and 300 selfies for the athletes in the Olympic village and the tv coverage of the Tennis stars make up for the cost? Also must be included is the opportunity cost of hogging limelight away from ordinary sportspeople. Imagine being a world beating, serious player of an obscure sport in the Olympic village. Then imagine you just got the loveliest date of your life because for once in your life your strengths helped you stand out. Now imagine she stood you up to wait in line to get a selfie with Rafa Nadal or Roger Federer. Still want them in the village?
Sorry about the rant. No, I am not an Olympic medalist who got stood up.