pain didn't even aim for his vital points so it was just a simple stab. And like in said afterwards he turned into the 9 tails. He can heal small wounds ofc but not big ones. Heck even Madara with Hashirama's sage mode healed a stab from Sasuke.
And how do someone's healing get better with an arm?
White zetsu's cell accelerates healing due to black zetsu modifying their dna to replicate hashirama's, you can read it on narutopedia actually. Reason why madara was able to heal the stab wound was because he had zetsu/hashirama's sage/dna. Pain did hit vital points, pain purposely hit those points to hinder naruto's movements. Anything that can be tampered with to hinder your movement anyhow is a vital point. Cutting a string of muscle in anyone's body can affect that part of the body which the muscle might be connected to.
Also naruto didnt necesarily die, he was unconscious after the extraction of the beast. here bro
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"Due to his Uzumaki lineage, Naruto possesses a powerful life-force and physical energy, giving him an extreme longevity, stamina, and vitality. From this, he could survive the extraction of a tailed beast (albeit he was rendered unconscious and in a critical state).[63] Naruto is also known for his greatly accelerated healing.[64] His lineage is part of the reason why he could synchronise with Kurama's chakra.[65] Part of his chakra prowess and physical energy stems from being a reincarnation of his ancestor, Asura.[32] Naruto's healing ability was further heightened after receiving a prosthetic forearm made from Hashirama's cells."