Part of the purpose of Hot Shot/Lead Shot is to also serve as a minor attention tax, where you have to mentally track the buff to make sure you're refreshing it on time. As a trade off, they have a very generous damage per execution time to make it worth your while.

If you've ever been distracted in a hectic situation and glanced back at the boss to see your Lead Shot has fallen off without you remembering to refresh it - that's a demonstration of it's purpose right there, it's a mechanic designed to reward attentiveness.