Honestly I think it depends on the character. I wouldn't think they would go that route with say Starlord or Dr. Strange. They would just recast.
But If Chris Evans died after Winter Soldier, I do believe there would be some discussion of having Bucky or Sam take over the shield. Because it was done in the comics, it becomes an option which at least deserves to be in the discussion.
And I'd say the same thing for Captain Marvel. If Brie died, I think there would be some conversation over having the young Monica we saw in Captain Marvel become her sucessor.
I'm frankly expecting Jane to take over Thors place and he's not even gone yet. That's the sort of thing that comes about when you incorparate a legacy character in the story. It's suddenly this potential option. We KNOW deep down it'll never happen in the comics... but because movies are a different medium where the status quo can change, it's taken a lot more seriously.