Corporate identity is not just a "logo-letterhead-business card". This is the whole appearance of the company, so to speak, "business packaging": from the organization's seal to the employee's badge, from the corporate font to the corporate website.
The logo is the main, but by no means the only element of the corporate identity. Usually it occupies only a small part of an advertising banner, website or some other point of contact of the client with the brand, therefore, to support the recognition and memorability of the latter, it is important to design all media in the same style.