Yes, carpeted stairs are generally considered safer than stairs with hard surfaces like wood, vinyl, or tile. Carpet provides more traction, which helps reduce the chances of slips and falls, and its cushioning can lessen the severity of an injury if a fall does occur. Hard surfaces often lack the friction needed for a secure tread and can be quite slippery.

However, it's worth noting that some carpets can also be slick, particularly if they are brand new, dirty, or made from certain materials. If any stair surface feels too slippery, traction treads can be added to most materials to increase grip and improve safety.

When deciding whether to repair or replace your carpet, consider its age, the extent of the damage, and its location. It's often best to replace the entire carpet if the damage is extensive, such as large sections needing replacement, or if it's caused by water, which can lead to mold problems. Similarly, if your carpet is nearing a decade old, replacement is likely the more logical choice. On the other hand, consider repairing your carpet if the damage is localized to one spot, like minor rips or snags, the carpet is still relatively new, or the damage is in a low-traffic area of your home.

A transition piece between carpet stairs and wood flooring isn't always necessary. A transition piece separates two types of flooring in between rooms and areas, like carpet and vinyl. Because the carpet on the stairs tucks into the seam, you can’t see the fringes, and there is no need to hide anything. However, you can use a stair cap if your stairs have a nose.

The cost to install carpet is $1,780 on average for 330 square feet, the size of an average living room. This cost could range from $200 to $5,000, depending on the amount of carpet, material, and type of carpet. 

If you need 500 square feet of carpet, it’ll cost $1,500 to $5,500, while 1,000 square feet of carpet costs $3,000 to $11,000. Polyester is one of the more affordable options, ranging from $1 to $3 per square foot. Wool is a more luxurious option, ranging from $4 to $20 per square foot.