Absolutely!
This is a point that tends to kill introverted/insecure people I think. They assume that asking for permission is making things easier for people, but there's a limit where you're not allowing others to delegate responsibility onto you. Your job is for others to not have to think about the things you take care of.
You’re conflating introversion with agreeableness and neuroticism or even social shyness. Introversion is its own aspect.
There's a difference between keeping someone informed and making them reown the problem