For those who used to the Win+Tab or Alt+Tab keyboard shortcuts to navigate through the running application Windows, the new Task View seems to be redundant and unnecessary in Windows 10. Unless you are really into the new virtual desktop, you can safely hide it from the taskbar and completely rely on the keyboard shortcuts instead. And of course, if you are using a tablet that doesn’t have a keyboard attached, you better keep it on.
To hide the Task View button from taskbar, simply right-click Taskbar, and uncheck the option Show Task View button.
The Task View button disappears from the taskbar right away.
If you also don’t like having the search box/button to occupy your taskbar space, you can also hide it by right-click Taskbar → Search → Hide.
The Search button disappears from the taskbar immediately. Now, the taskbar looks a bit cleaner with 2 less icons.