One-piece shaft collars can potentially damage the shaft surface, but this largely depends on the material of the collar, the material of the shaft, the application, and how the collar is installed and used. 
Shaft collars are typically used to position, locate, and retain components on a shaft. One-piece shaft collars are designed to provide a secure fit by clamping around the shaft. They are generally made from materials such as steel, stainless steel, aluminum, or plastic. The risk of damage to the shaft surface is influenced by the hardness and finish of both the collar and the shaft. 
If the collar is made from a harder material than the shaft, there is a higher likelihood of surface damage, especially if the collar is over-tightened. This can lead to indentations or scoring on the shaft surface. Conversely, if the collar is made from a softer material, it is less likely to damage the shaft, but it may wear out more quickly.
Proper installation is crucial to minimizing damage. Over-tightening the collar can cause excessive pressure on the shaft, leading to deformation or surface damage. It is important to follow the manufacturer's torque specifications to ensure the collar is securely fastened without applying excessive force.
In applications where shaft surface integrity is critical, such as in precision machinery, it may be advisable to use shaft collars with a protective inner lining or to select collars specifically designed to minimize surface damage. Additionally, regular inspection and maintenance can help identify any potential issues early, allowing for adjustments or replacements before significant damage occurs.
In summary, while one-piece shaft collars can damage the shaft surface, careful selection, proper installation, and regular maintenance can mitigate this risk.