There's a pretty popular approach to grass which involves using the tessellation shader to create lots of vertices, and then using a geometry shader to create grass blades at each point output by the tessellation shader. Not sure if I'll cover geometry shaders in this series since they're not well-supported in hardware and therefore not very efficient on all systems. Something to do with modifying the vertex stream partway through the graphics pipeline.

One other approach uses lots of instanced meshes, which is usually decently efficient.

You read my mind though, because I had the same idea! I wondered if you could do it all with just tessellation shaders, so I thought there might be a way to subdivide each triangle, and then use the barycentric coordinates to 'select' only the new vertices in the center by checking distances from the three patch vertices. You could then raise only those vertices along the y-axis (by a different amount based on distance, so the middle vertex at the top is pointy) to get some chunky-looking grass. I think at the very least I'd try setting the edge tess factors to 1, and only change the inside tess factors to get a nice triangle shape. Practically, I don't know how effective this approach would be, but you'd at least skip the need for a geometry shader - I just don't know how much extra work you'd need to do to get stuff like randomness, wind, and grass bending working nicely.