Nothing wrong with that, look up “coffee sock”. It’s used exactly as you describe, except they put this filter down first, then lift it out with the grounds after it’s done brewing. All the other methods mentioned here are valid too, coffee is coffee!
For what it’s worth, wetting paper filters is usually done with near boiling water in the chemex, so it IS preheated with the regular process. Preheated steel also won’t retain as much heat. I don’t disagree with your post as written, it just doesn’t match the reality of what’s usually done