What are the reasons why warring nations’ goal is for taking the capital of their enemy group over?

In a war you want to consider strategic points to take. So let’s say a battle takes place next to a bridge. If your army controls that bridge than you have a higher chance of victory since you get to decide who crosses and who doesn’t. Now when an army takes over an entire city, than that army can use the assets to its advantage. (Factories, roads, rail roads, runways, etc.) but when that city is the capital city, then that country loses its command and will most likely dissolve.