I have never in my life heard of giving pain medications to a cat after a neuter (which is a non-invasive surgery) or a spay which is more Invasive. Nor have I witnessed any of my cats showing signs of pain after a normal spay or neuter. So that is one medication you should say "no thank you" to. That is pure going for your wallet.
Males can safely be neutered at age 8 weeks. Femals can be spayed at 3 months. There is new technology for males only and I don't know where it is being used but it involves shrinking the testicles instead of surgery. Jan knows more about than I do. I will send this post to her! She can enlighten us on the newest procedure though I don't know that it is being used really anywhere..