@Cycloptichorn,
The only rule that the Engineers Corp taught me was that the invading army stands to lose more than the defenserd who are dug in.
The military strategies are always fighting the "last war". Today we have several levels of technology that make the "high ground" axiom a thing of the past.
Anyway, in the battle of Chatanooga the CSA was swept away in a day each from their high ground positions in the "Battle above the Clouds" and on Seminary Ridge.
The Vicksburg Campaign had the give and take of several hilltops until the actual siege and capitulation by the CSA. j Johnston had decreed that Vicksburg was indefensible so Grant capitalized on sveral errors ( and suffered from indecisiveness of a few of his own generals) but hills were traded like baseball cards until Johnston figured he could get really good terms if he surrenedered on July 4 1863.
Hills often merely focus the attacks (if competently done). HOWEVER I dont include Longstreets "charge" at "The Angle"on July 3 of Gettysburg as anything but incompetence. Here was a hilltop that was merely a well defined shooting gallery for Union artillery and riflemen. (If youve ever been to Gettysburg and looked over the ground, you would see).