Mesh shaders are more than just having control over the input format or the topology.
I agree that it's only one part of what they can do. That doesn't conflict with the observation that it is something that primitive shaders do not match. I'm stating my interpretation that it seems that what AMD uses as primitive shaders appear to be distinct in many ways from what mesh shaders are defined as. The vendors took a general premise of using more compute-like shading and decided to optimize or change different elements of the setup process, and they are compatible or incompatible with different things as a result.
From the differences in input, usage, and compatibility, I get the impression that they aren't the same thing.
In fact having control over the input format isn't all that useful since it's very hard to beat the hardware's input assembler.
I think this goes to whether you want to take the stated reasons for mesh shaders at their word, since it's how the index processing portion of input assembly is being replaced.
I agree that replacing the hardware has proven difficult, since even improving it was unsuccessful with primitive shaders in Vega. However, that portion of the pipeline is where the serial bottleneck and flexibility concerns are located that the mesh shader proposal cites as its reason for being.
If primitive shaders do not share that reason for existing, that's another difference.
It's probably because of hardware bugs rather than anything architecturally specific ...
There are a lot of individual reasons for the profile changes, some based on games that do not use API commands properly, or architectural quirks that make certain features a performance negative.
They are too low-level and product specific in many case to be appropriate as API-level considerations, which is what mesh shaders are.
Geometry shaders or the tessellation stage can potentially output an 'unknown' number of primitives and this is highly problematic with transform feedbacks since the hardware would have no way of corresponding the primitive output order with the primitive input order.
Nvidia and Microsoft would agree with this, and their response was to dispense with those stages. Nvidia still gives tessellation an ongoing role for being more efficient for some amplification patterns, while Microsoft in the passage I quoted has stated what they plan for the tessellator.
Ordering behavior is an element many proponents of a completely programmable paradigm have neglected, but it still leaves a distinct difference where primitive shaders can have stronger ordering because they feed from that serialized source, and mesh shaders do not.
Primitive shaders with hardware support for global ordered append is currently the viable path that offers mesh shaders to be compatible with the traditional geometry pipeline.
Perhaps that will be put forward in primitive shaders 2.0 and mesh shaders 1.x, as I haven't seen the various parties involved committing to this publicly.