If you think Cold Harbor was a one off then you mis understand the whole campaign of 1864. The campaign from the blue side was frontal attack which was repulsed then to the left march all the way to Petersburg. Cold Harbor was just the worst of them so it gets the most publicity. John Hood would have done the exact same thing as Grant.
The only difference is that when all was said and done, by the end of the overland compaign in early summer, Bobby Lee and the shattered remnants of the once vaunted Army of Northern Virginia, were penned up like rats in a cage in Petersburg, VA. There it would languish for many months, until a desperate attempt at escape was made in early April 1865. Within in a week or so, General Lee would surrender the few survivors of the ANV to Lieutenant General Grant.
John Hood never won a campaign as an army commander. Grant never lost a campaign as an Army commander.
I think one thing that set Grant apart from the rest is he didn’t turn back.