Does IoC with constructor injection in asp.net mvc controllers waste resources?

I'm not sure if its just me, but I get the feeling that constructor injection used in ASP.NET MVC controllers is causing unnecessary resource consumption.

Components that's not being used for a particular web request still needs to be created when controllers are created. It's like buying booth milk and juice when I'm thirsty for milk and then I just throw away the juice.

Compare these examples of constructor injection and service locator for controller to clarify my concern.

Constructor Injection, booth deps are created but only one is used.

public class MyController : Controller
{
    private readonly IDep1 _dep1;
    private readonly IDep2 _dep2;

    public MyController(IDep1 dep1, IDep2 dep2)
    {
        _dep1 = dep1;
        _dep2 = dep2;
    }

    public ActionResult Index()
    {
        _dep1.MakeStuff();
        return View();
    }
    public ActionResult PageTwo()
    {
        _dep2.MakeStuff();
        return View();
    }
}

Service Locator, each dep are created only when its being used.

public class MyController : Controller
{
    public ActionResult Index()
    {
        var dep1 = ServiceLocator.Resolve<IDep1>();
        dep1.MakeStuff();
        return View();
    }
    public ActionResult PageTwo()
    {
        var dep2 = ServiceLocator.Resolve<IDep2>();
        dep2.MakeStuff();
        return View();
    }
}

PLEASE NOTE that an IoC container (which is beneficial for many reasons) can still be used for the Service Locator pattern. I do not want this to be a discussion around IoC and container frameworks neither other benefits from constructor injection (clear visibilty of dependencies etc). It's the constructor injection pattern and how it wastes resources in ASP.NET MVC controller situations that is my concern.

I guess the main question here is: Is Service Locator a