The stairs in your home can actually be quite dangerous for yourself and your family members, especially if you have small children or older ones staying in your home. There is always a risk of them falling up or down the stairs and hurting themselves on the sharp edges of the stairs. So to lower the risk of someone falling, install carpeting on the stairs. There are many safety benefits to this beyond just added grip. Carpeting creates a softened curve on the nose of each stair, so if someone does fall, there is a lower risk of them harming themselves on a sharp edge.
Additionally, you should always make sure that you have a railway next to your stairs to ensure you and anyone in your home have something to grip onto when coming up or down the stairs. Even though carpets are more challenging to clean than bare steps, it is a worthwhile trade-off if it saves someone from getting seriously injured.