As an example, which can apply to other situations:
I have a character. It is rigged, it has shape keys, it has materials assigned to various polygons, there are drivers attached to all of the above in various ways.
I wish to copy the mesh. When I hit paste, i want only the mesh to be the result. Not also the rig, the materials, the drivers, the shape keys, etc etc and freaking etc.
How is this done?
Easiest way? Export it as an FBX and reimport
Please tell me the solution is not that stupid…
(I’m guessing that it is, otherwise you would have typed a different solution.) 
It wouldn’t be too difficult to write a script that removes all drivers, animation data, vertex data, and shapekeys… but the exporters already do that with the right settings, so why reinvent the wheel? Actually, your best bet would be OBJ, that will strip pretty much everything except the actual mesh.
Note that this will remove modifiers as well- I really do mean everything, all you’ll have left is vertices/edges/faces
Use any simple mesh (for example the “default cube” ) and select the wanted mesh data.
Nothing else will be “linked” and make it single user…
Now the cube has the Suzanne mesh.
…hate to say it, but maybe Geometry Nodes?
At least it definitely won’t copy the rig, mods and drivers… probably no shapekeys either…
If you duplicate the .blend file i think you can append meshes only from it, try it.
Thanks for all the tips; I’ll try them and see which one works best for me.
Seriously thought there was just a menu command somewhere that I didn’t know about, as this is just such a … basic thing in the first place…
This will copy across shape keys though. That said, it’s a simple mater of deleting them to get back to the basic mesh.
TBH… i didn’t checked everthing… but then shapekeys are part of the mesh… so to speak…
Little video:
Duplicate the object, remove modifiers, unparent, convert to mesh the mesh which if recall this removes shape keys and applies modifiers almost instantly (if that’s not wanted then remove selected modifiers manually) and any drivers on the shape keys would go away, but I don’t think the properties or transform panel drivers if any.
Ha - that’s pretty much what I’ve been doing…remove everything possible, then copy to a new scene.
Which ends up working, but a “copy/paste mesh” function would be far faster.
Export > import is four clicks, how much faster do you want 
I suppose I could whip up a script for you that would take only two clicks or a keyboard shortcut
Yeah, the OBJ loop ended up being the cleanest route i think. Has those various checkboxes to “only this , not that” which helped quickly knock out some unwanted particulars.
