A generalist is a breadth based person who can coordinate and collaborate in daily operations and strategy but cannot add value beyond a point as they lack strategic know-how or depth. Since it is a coordinator-collaborator (Program Management+Sounding Board) role, it is more of a will and less of a skill game. Hence, the endless supply of junior folks can always end up doing the generalist roles.
This essentially means that your role would never be valued as there will always be a cheaper/inexpensive alternative to you.
Hence generalist roles won't be able to succeed unless they specialise in something and become T-Skilled.