What you are describing is how it works. A mesh shader is a lot more general and flexible than even all three of Vertex / Tessellation / Geometry shaders workin

What you are describing is how it works. A mesh shader is a lot more general and flexible than even all three of Vertex / Tessellation / Geometry shaders working together. And so, it replaces all three of them to be an alternate pipeline option. It cannot be chained together with them.