Generally, available mouthwashes have very low percentages of hydrogen peroxide. Therefore you should use it regularly for a very long period to get some results, and even this would be minimal.
Most ready-to-use mouthwashes recommend a rinse time of 30-60 seconds twice a day for a few months. I doubt that there would be a real whitening effect at the moment given the low hydrogen peroxide concentration, so in this sense, it makes no sense to use long-term whitening mouthwash.
These mouthwashes can also be slightly irritating to the skin in your mouth, so using them for months or years can irritate your mouth.
It is better to use mouthwash with a good fluoride content, which can help to stabilize the PH in your mouth and prevent cavities.
Many types of mouthwash contain alcohol that can cause a burning effect in your mouth. Alcohol can strip the skin in your mouth and create a drying effect that is bad for your mouth in the long term.