aura: Make aura::TooltipClient completely static?

ui/aura_shell/shell.cc

Index: ui/aura_shell/shell.cc
diff --git a/ui/aura_shell/shell.cc b/ui/aura_shell/shell.cc
index ded7967c1defb0547c5f3c8141d6b4d95f4309f2..750b174834c5cf10a61cf03c60fa6360d471a3f5 100644
--- a/ui/aura_shell/shell.cc
+++ b/ui/aura_shell/shell.cc
@@ -125,8 +125,7 @@ Shell::~Shell() {
   // ShellTooltipManager needs a valid shell instance. We delete it before
   // deleting the shell |instance_|.
   RemoveDesktopEventFilter(tooltip_manager_.get());
-  aura::Desktop::GetInstance()->SetProperty(aura::kDesktopTooltipClientKey,
-      NULL);
+  tooltip_manager_.reset();
 
   // Make sure we delete WorkspaceController before launcher is
   // deleted as it has a reference to launcher model.
@@ -142,8 +141,6 @@ Shell::~Shell() {
     delete child;
   }
 
-  tooltip_manager_.reset();
-
   // Drag drop controller needs a valid shell instance. We destroy it first.
   drag_drop_controller_.reset();
 
@@ -229,8 +226,6 @@ void Shell::Init() {
 
   // Initialize ShellTooltipManager
   tooltip_manager_.reset(new ShellTooltipManager);
-  aura::Desktop::GetInstance()->SetProperty(aura::kDesktopTooltipClientKey,
-      static_cast<aura::TooltipClient*>(tooltip_manager_.get()));
   AddDesktopEventFilter(tooltip_manager_.get());
 
   // Initialize drag drop controller.