Not going to lie, as soon as you mentioned LC I was disinterested. But your suggestion sounds good. A few easy/medium questions and maybe the ability to Google sounds fair. I sort of enjoy basic fizz bang code screenings.
And just to be clear I'm only suggesting it for junior positions. Most of the time I think you can suss out whether someone can code by discussing their direct contributions to previous projects. If not, you can always do one LC problem.
I see it as a great way to just run a sanity check that this person who graduated from Random State six months ago can actually code, and as a great way to ensure high quality very senior people refuse to go through your interview (unless you're paying FAANG wages).