Puerilis
Angel of the dark rose
Actually, it is kind of like a vaccine. They inject some of the virus into your body so that the body can build up it's antibodies against the virus. When you finally do get the virus, your body already knows how to kill it. Although it does make you kind of sick for a while.
Steel is Always Inpure. There is no such thing as "Pure" steel.
I do believe that was the point.
Purity of the body, especially in lit, is always symbolic. Theres no reason to debate the literal concept of purity on earth, because scientifically it's been proven that the 'concept' of purity is not benificial, as is seen with the reference to steel. Of course that scientific fact becomes a literary device in Alita (which I've never read, so I'm speculating on your post alone).
Literature has always investigated the meaning of purity, in all it's forms. Most lit comes close to your conclusion. Purity of soul is always sullied or not so great after all. Purity of mind is either boring or a fraud.
Purity of will is sometimes veiwed skeptically too. I don't know about Alita, but many stories equate 'conviction' with 'fanaticism'. The problem is that purity is at the far end of the specturm. As a concept, it is the polar opposite of utter corruption, and most lit doesn't approach the human condition from that sort of contrast. Any character that grows hast to have both in him, so if Alita can't be pure, it's indictive of her constant need for growth, and the fact that she can never attain, only strive for.
This is all speculation based on the basic symbolism that comes with purity, so it would be interesting to see if anything in the manga coincides with what I've said.