I'm sorry, but you didn't answer my question, and your suggested fix didn't work. In the Finder, every window has a "view" gadget in the toolbar, and it offers four choices, including Cover Flow. That hasn't changed.
The problem occurs in any File Open dialog from within an application. In a File Open dialog, it shows a view resembling a Finder window, but in File Open it shows only three choices instead of four: Icon view, list view, column view, but no Cover Flow view.
Please follow these directions: Preview, File, Open. Then tell me what you see. I see a three-option View gadget, with no Cover Flow option.
Just to be sure, I followed your directions. I used Customize Toolbar. I removed the View gadget completely. I opened a new window to make sure it had "taken:" no View gadget. I Customized Toolbar again. Added the View gadget back. Opened a new window: View gadget is there, with all four choices.
I then performed a File, Open from within an application. Again, there is only a three-choice View gadget.