Is $10,500 to install Shaw Awaken Spirit ii nylon carpet a fair price?

I need to choose between two carpet options for my home. My family consists of 6 people (Mom, Dad, Grandma, and 3 kids aged 4, 2, and newborn). The carpet will be installed upstairs in 4 bedrooms, a hallway, and stairs, and in the basement for stairs, 2 bedrooms, and a living room (in-law suite). I am hoping to keep the carpet for 10-15 years. I was initially leaning towards polyester due to its lower cost, solution-dyed nature, and perceived stain resistance, but I've heard concerns about crushing and matting. Now I'm considering nylon, but I'm worried about potential stains from my kids, such as red pasta sauce or yellow vomit. I'm willing to pay the $3,000 premium for the nylon option if it proves to be a better product overall, especially regarding stain resistance and durability.