Spotsylvania C.H. proves my point. Grant hits a wall there and instead of grinding it out he wheels left and keeps going stretching his his supply chain to the breaking point. Why? He wanted to take Richmond for his top hatted Fuhrer.
The Union supply chain was never an issue. Why did Grant move to the left? Because he knew Lee would have to move with him. Lee would have to be reactive and not proactive and Grant would have the initiative. And yes, Lee would have to worry about Richmond - Comrade Davis would make sure of that. But in the end it all wound up at Petersburg and not Richmond. If Richmond had been Grant's aim then all he needed to do was shift to the right and take it once he had Lee bottled up. But it was Lee's army and not Richmond that was Grant's goal.