Your problem is that you are adding an item that is not the same as the Select Features
on the Tools
toolbar. The Select Features
from the Data View Context Menu
is the tool that one can start once right-clicking in the data view.
What you are looking for is tools under Selection
category:
Unfortunately, you won't be able to have the same drop-down menu of the tools to pick from (by lasso, polygon, line etc) because this is done by some custom ArcMap UI code that is not exposed through Customize
menu.
The closest you can get is either to have just Select By Rectangle
(which is the default for built-in Select Features
group tool) or to add multiple selection types to the toolbar: