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of course the issue with your theory is... the extra damage as chaos damage only applies to hits, not to damage over time...
You're right because he's using essence drain, all other dots in the game scale from the base hit application.
If he wants to scale dots, he should probably not look at essence drain as his main source of damage and as a secondary source of damage.
There's no raw DOT scaling in the game unfortunately, DOT's scale from base hits.
@OP, consider going infernalist witch, get the internal flame perk whatever it is, then the one on the left that allows you to apply ignite and ignite magnitude from any and all hits.
If you go bloodmagic node, you're perma considered in high flame mode, so all your hits always will ignite enemies.
If you want to stick with the chaos theme, get the blackflame ring, it cuts ignite duration in half, but doubles the DPS and turns the ignite damage from fire into chaos.
Your essence drain would proc ignite still this way, but you'd be better off doing higher base damage hits for the ignite considering that's how DOTS scale.