Junior level developers at companies I've worked at are often taught to run meetings as part of helping them grow. If a couple junior developers work on a project then having them take turns facilitating the meeting was common. My team's meetings at my last company we also had everyone take turns facilitating it. There were some pre-meeting tasks that the facilitator was also responsible for like organizing some documentation related to last week on-call alerts + commenting on any product metrics for the main product we worked on (most of the time it was looks normal).

A lot of growth I've seen is about having people get opportunities to do things more commonly done by people at higher levels. While most design documents are written by seniors or above sometimes mid level/junior engineers get an opportunity to write one and all design documents get a lot of feedback anyway.

That doesn't make sense, leading meetings is a basic skill. Unless you mean something else then what I think you mean by meetings. This is stuff we've been doing through high school and college doing stuff like group project meetings. Personally I've lead meetings at all levels in my career so far

I think the author means "senior" as a concept (For varying levels of seniority, from senior, to staff, and beyond.) and not just a point on a progression path.

#1 Running meeting and knowing how they work is a really good skill for every one to have