To resolve disputes over line calls, we often replay the point. Can't get much fairer. That said, however, a replay can often paper over the underlying issues and perversely increase rather than reduce future challenges.
Yes, it is poor etiquette for players to persistently challenge outcalls. And most assume here that players are disputing the accuracy of the call, namely was the ball actually in or out.
In many cases, however, it is more nuanced than that. When questioning an outcall, a player may not necessarily be saying I can see the line better. He or she is just as likely saying:
(a) in these particular circumstances;
(b) it's very close;
(c) no one can be 100% certain either way; therefore
(d) I should receive the benefit of the doubt and the ball be called in.
So, how to address such a complex and lengthy appeal?
Without an umpire, line judges or video replay, the primary social tennis convention must be the receiver alone calls the ball in or out. This is also the case for double bounces, hitting the net, breaking the plane of the net, double hitting a ball, etc. These are all calls necessarily made from the one side of the net. The only exceptions are if the ball bounces under or goes through the net when it becomes the opponent who makes the call.
The second, balancing convention is when the receiver is at all uncertain that the ball is in or out, the benefit of doubt must be given to the opponent. This is the benefit of the doubt convention, also one of the mainstays of social tennis. See among many others:
Thus if the ball clips a line or just misses, there should be no controversy, as the receiver must be uncertain and is expected to give the benefit of the doubt to his/her opponent.
Some players, however, minimise their personal zone of uncertainty, often down to zero. They "call it as they see it", believing they can tell if a ball clips the line or just misses. In fact, they're guessing and they're kidding themselves. The research makes this clear.
To start, because they are in motion receivers are generally the worst at calling the lines as compared to line judges, umpires or even spectators (see for example Vault - who can see best.
Secondly, we almost never see the actual point where a ball impacts the court, as the ball is moving way too fast. Our eyes see the ball approach and then leave the court but we don't see the bounce itself - our mind fills in the gap. See this video as to Why we make bad line calls.
Then to make matters worse, there is a standard perceptual bias shifting the impact point of a ball in the direction of its motion. That is, we all tend to 'see' a close ball out rather than in. See Perceptual Mislocalization of Bouncing Balls
And lastly, modern psychology notes that players often see it as they wish it to be, not as it really is. For example, there is a confirmation bias where we expect a ball to be out and don't play at it, but topspin brings it in at the last moment - maybe - and we still manage to wish it out.
G Mather in his study Perceptual uncertainty and line-call challenges in professional tennis gives us a rough estimate for the professional zone of uncertainty. He flags that wrong calls can sometimes occur in a 10cm zone but notes that line judges and professional players are very good within "a few centimetres". He concludes:
Professional players and line judges are remarkably proficient at judging ball bounce position, displaying accuracy of just a few centimetres. Ball bounces near the base and service lines are more difficult to judge than those near the side and centre lines, probably due to retinal speed of the ball and greater perceptual uncertainty along its trajectory. The model predicts that 8.2% of all line calls involving balls within 100 mm of a court line will be called incorrectly by line judges, due to inherent limitations in their perceptual system.
So what about players on the other side of the net? In fact, the opponents can often know when a receiver is guessing about their line calls. There are several clues, most notably when a caller has a poor view, such as:
(1) calling across a far line;
(2) calling a ball out over the baseline when looking back from the net,
(3) dealing with a ball at their feet on the baseline; or
(4) calling a serve long or wide when it's really partner's call.