It's not arbitrary. Each attack roll at the table corresponds to a meaningful attempt by the character in the fiction to defeat the ogre. This is spelled out in the Basic PDF (pp 69, 71-72):
On your turn, you can move a distance up to your speed and take one action. . . .
The most common action to take in combat is the Attack action, whether you are swinging a sword, firing an arrow from a bow, or brawling with your fists.
With this action, you make one melee or ranged attack. . . .
Whether you’re striking with a melee weapon, firing a weapon at range, or making an attack roll as part of a spell, an attack has a simple structure.
The point becomes even more evident if we imagine the fighter attempting to kill an ogre with an arrow rather than a sword.