I'm actually speaking from a Gunslinger viewpoint, since it's the class I use mainly. Since Tripmines are inconsistent af, I switched to Incendiary. Since Knife Juggler is no longer consistent, I switched to Incendiary Blade. Without the DOT on these it would make ability kills quite a bit harder.
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I use both gunslinger and sunbreaker and taking the burn away from incendiary would be huge. the burn on incendiary is good now without the burn it will ruin incendiary.
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I forgot about gunslinger burn. Probably because it has almost zero impact on my crucible experience.