Players generally stand in the middle of the baseline to warm up before a singles match. However, it is rare that both players are standing in this position during an actual point.
In singles, the server will be slightly to the right or left of the center of the court and behind the baseline. The player returning serve will be close to the singles sideline and could be either well behind the baseline, close to the baseline, or inside the baseline. There may be times when the player ends up close to the middle of the court as their opponent is hitting the ball, but they will likely be a little shaded to one side or the other depending on the last shot that was hit and the anticipated reply. Unless both players are hitting the ball right down the middle, they will not be standing directly in front of each other in the middle of the court near the baseline.
All points start in a diagonal direction and tend to be played away from the middle of the court. Players can look incredibly good when standing in the middle of the court hitting back and forth during practice. The same players who look adept at striking the ball in this situation often become much less impressive when an actual point is going on. The balls are coming from all different angles, at different depths and are often hit away from the player. If you are practicing for singles without serving and returning serve, I recommend that you start with both players diagonally across from each other, both on deuce side or both on ad side, hitting balls to an area you would target in an actual point.
It is very important to simulate what happens in a match when you are practicing. Position on the court often determines shot selection. Practice using the starting position you assume in an actual point to give yourself the best chance for the results you want in a match.