My whole coaching career has been a battle with the stopwatch. This simple piece of technology embodies both the biggest strengths and weaknesses of our sport. Swimming is simple, and you know who is "better" because the clock tells you. But our obsession with what we can measure in swimming is also a huge distraction from how to get there.
This might seem like a curious position from someone who has passionately advocated for race pace training. After all, if you're training race pace, isn't it important for swimmers to know the precise pace they are swimming? Won't the need for that precision grow as swimmers get faster and faster?
The answer to both questions is no. If swimmers learn to rely on their coach for a precise reading of their time, they will not develop their own skills for judging how well they completed the rep. The faster the swimmer, the more they get a sense for what their times in warmup or a practice "mean" for performance. The tendency to focus narrowly on this one measure can be very destructive to an elite swimmer's progress.
My first rebellion against the stopwatch as a coach was to stop the time honored practice of timing 25 sprints on meet day.
I found that there were no good outcomes from telling swimmers how fast they went on pre-meet 25. They either swam "slow" and this made them doubt whether they could have a good performance, or they went "fast" and felt the weight of subsequent expectations.
As a coach, you don't want swimmers focused on either. You want them focused on "what do I have to do to have a good result" (process). On meet day, that can still mean a 25 for time, but the coach and swimmer should judge it not by seconds and hundredths but a meaningful execution of what the swimmer wants to execute.
Likewise, in practice, you want qualitative feedback to dominate the conversation. If significant time is spent spitting times back at the swimmer, it is time when you could be praising them for stroke corrections, suggesting new avenues for improvement, or offering encouragement.
Again, it's useful to imagine this teaching style in another context. Imagine your math teacher giving you a graded quiz every few minutes in class- wouldn't you rather they spent the majority of their time teaching you how to do problems rather than evaluating how good you are at solving them?
If you absolutely need to, check in with the old watch now and then to see whether you are headed in the right direction. Otherwise, please for the love of all that is good, watch them swim and give them what they need to improve.