Should intended major choices impact essays?

Depends on the essay. If it’s something like “why did you chose your major”, probably.

If it’s “Recount a time when you faced a challenge, setback, or failure.” it can be about anything. Unless the best story you can tell is about an Electrical Engineering failure, you shouldn’t try to force it to be about your major.

A vast majority of essays are attempts to learn about you as a person.