Unity and other dependency injection containers automatically do this. When you inject a service into a controller, it will automatically resolve the entire dependency graph of that service. Not only can you resolve dependencies of the service and its dependencies, you should inject dependencies into the service that needs them instead of the controller.
Any class (including the controller) that has more than a handful of dependencies is a code smell that you are violating the Single Responsibility Principle, and you most likely should refactor to aggregate services.
And yes, injecting the container to any point outside of the composition root is an anti-pattern called a service locator.
As for injecting services outside of the controller, it is important to distinguish between injectables and runtime data. For example, some try to inject services into DTO objects, attributes, static classes/extension methods, and other places where it is anti-pattern for services to be injected. For these situations, it is important to properly assess the situation and refactor toward a DI-friendly solution - favoring constructor injection over other alternatives and considering a service locator as a last resort. For example, if you are trying to make an extension method with a dependent service, most likely you have some functionality that itself should be a non-static service, DTOs should never be created from a DI container, and you may have to make use of more than one extension point in MVC where you inject the container within the composition root of the application, which does not constitute a service locator.
Is it worth it? Usually. What is gained? You gain the ability to change the application much more quickly than if you have a tightly-coupled application in ways that the designer of the application may not have even anticipated. So the extra cost of ensuring the application is loosely-coupled is usually more than recouped in ongoing maintenance of the project. As a side benefit, you gain the ability to easily unit-test each component independent of the others.