I don't agree with the multiple project aspect. If a senior designer is doing the actual production of design on a project, and it is a big project, splitting time across multiple projects would be irresponsible.

As far as the discussion goes, I think it's two things:

1. The senior designer will have a better designed outcome, but more importantly will get there through a more practiced (experience) process and will do so faster (more efficiently) than the mid-level designer. And, they have the ability to share this knowledge with others.

2. They have the experience. It's simply irreplacable. When you work bigger and bigger projects, what you learn is managing people skills and learning how to communicate the decisions that lead to your designs.

As an example, everybody is a critic as soon as a new logo/rebrand comes out from a big brand. The outcome is heavily criticized, but a lot of the criticism comes from people that aren't familiar with the politics and committee decision making that goes into any rebrand of that scale. Perhaps, somewhere along the way, the designer may have lost a battle on design vision with the client. Sometimes, its inevitable. But as you become more senior, you learn tricks to minimize this.

TLDR: A mid and senior designer may design the same thing, but the senior got there through a more proven process and is able to talk to the design decisions so that they are implemented to his/her vision.