No, the use of capos does not wear out your guitar strings. In fact, the tension applied by capos on your strings is not sufficient enough to break them. However, overtightening them on your strings will surely cause them to break.
This is primarily because guitar strings are already under tension on two sides – on the bridge on one side and the nut and tuning keys on the other. The tensile force absorbed by the string increases when the capo is overtightened, resulting in string breaking. This makes it important to apply only enough pressure on your capos for it to grip your guitar’s neck and fretboard and for the strings to be firmly pressed down the fretboard.
Leaving the capo on for long periods without using the guitar, such as playing with a capo at night and putting your guitar in its case with the capo still intact on the fretboard until the next day, is one action that will undoubtedly damage and wear out your guitar strings, fretboard, and tuning keys. This will have a detrimental impact on your guitar’s parts, as the high tension will cause your strings to wear out much faster.
Another consequence is that your capo’s tension mechanism may loosen, resulting in insufficient pressure to perform its function.
Because of the pressure of keeping the strings down overnight, your capo’s paddings will wear out and develop large tracks and grooves. The pressure exerted by your capo may leave scratches or dents on the neck and fretboard of your guitar. All of these negative effects on your guitar are why you should never leave a capo on for an extended amount of time.
Although strings are inexpensive and easy to replace, this does not mean that capos should be used carelessly. Remember that capos can damage major parts of your guitar like the neck, fretboard, nut, and tuning keys, so it’s critical to place them correctly and remove them carefully to avoid any unwanted consequences, especially since the parts mentioned aren’t replaceable and would require you to buy a new guitar.