I moved this to feature request

Actually I achieved desired behviour by implementing custom component based on page tree. It looks just like page tree but has root "For all sites", contains blocks and media and icons are displayed there.

Component declaration:

using EPiServer.Core;
using EPiServer.Shell.ViewComposition;

namespace Project.Web.Widgets
{
    [Component]
    public class AssetsContentTreeComponent : ComponentDefinitionBase
    {
        public BlocksContentTreeComponent() : base("epi-cms/component/MainNavigationComponent")
        {
            LanguagePath = "/episerver/cms/components/pagetree";
            Categories = new[] { "content" };
            Settings.Add(new Setting("repositoryKey", AssetsTreeRepositoryDescriptor.RepositoryKey));
        }

        public override string Title => "Assets tree";

        public override string Description => "Managing assets content in a tree view.";
    }
}

And descriptor for it:

using System;
using System.Collections.Generic;
using EPiServer.Core;
using EPiServer.ServiceLocation;
using EPiServer.Shell;

namespace Project.Web.Widgets
{
    [ServiceConfiguration(typeof(IContentRepositoryDescriptor))]
    public class AssetsTreeRepositoryDescriptor : ContentRepositoryDescriptorBase
    {
        public static string RepositoryKey => "AssetsTreeRepositoryDescriptorKey";

        public override string Key => RepositoryKey;

        public override string Name => "Assets tree";

        public override IEnumerable<Type> ContainedTypes => new[]
        {
            typeof(ContentData),
        };

        public override IEnumerable<ContentReference> Roots => new[]
        {
            ContentReference.GlobalBlockFolder,
        };

        public override IEnumerable<string> PreventDeletionFor => new[]
        {
            ContentReference.GlobalBlockFolder.ToString(),
            ContentReference.WasteBasket.ToString()
        };

        public override IEnumerable<string> PreventCopyingFor => new[]
        {
            ContentReference.GlobalBlockFolder.ToString(),
            ContentReference.WasteBasket.ToString()
        };
    }
}

I referenced these sources:

https://github.com/Geta/Epi.UnfilteredContentTree

https://www.epinova.no/en/blog/custom-icontent-with-its-own-navigation-pane/ 

Great!

But I still keep it here since it should be a built in feature

From EPiServer.CMS.UI 11.13.0, the statuses are available for assets pane too.

https://world.episerver.com/documentation/Release-Notes/ReleaseNote/?releaseNoteId=CMS-12249

EPiServer.CMS.UI 11.13.0 should be available on the NuGet server on Monday, November 19.

Great news!

Thanks!