Kendo grid does not allow all columns to be hidden from column menu as it disables the check box for last column in column menu.
But if we set hidden = true and menu = false properties for column, grid hides that column from grid and column menu, but enables the checkbox to hide all columns from grid leaving it empty. After which we can't get back the columns in grid which isn't valid.
Grid should always allow at least one column to be included in grid/menu.
Please find attached screenshot and below sample link.