“Let’s say they take Kherson. What do they win militarily that gives them an advantage?”
Kherson is a Ukrainian city. Retaking it for Ukraine is the objective and the advantage is in denying it to the invaders.
Also the Ukrainians have used HIMARS to damage the bridges across the Dnieper enough to prevent trucks from crossing but not soldiers on foot. If the Russians evacuate the area west of the Dnieper river, they will have to do so without their equipment and ammunition. The Ukrainians already know how to use all that equipment.
The Ukrainians could gain control of the dam over the Dnieper and cut off the supply of water to Crimea. This would mean the population of 2 million would no longer be roughly self-sufficient in food production but be dependent on food brought in by the Russians. This would put more stress on the Russians logistics.
“Kherson is a Ukrainian city. Retaking it for Ukraine is the objective and the advantage is in denying it to the invaders.”
What a terrible excuse. There’s no military advantage mentioned at all. Russia’s strength is heavy artillery with longer range than Ukraine’s and now soldiers will be holed up in a static area that can be pummeled at will and those soldiers will just have to take it, can’t even return fire. This sounds like a terrible use of personnel.
Control of the Dnieper River exit. It’s a big deal.