Is there such a thing as a text-only computer display?

Yes, but not as a normal modern monitor. A dedicated alphanumeric LCD, segment display, or split-flap-style display could show only characters. These are closer to specialized hardware than a regular computer screen.

The simplest software option is to run a terminal or command prompt fullscreen. That gives you a text-only experience, but it doesn't prevent the system from opening images or videos if you choose to do so.

You could connect a dumb terminal or text-only display to a computer and use a shell. The terminal itself would only show text, although the computer running it would still be capable of displaying graphics elsewhere.

Older teletype terminals and dedicated character displays are the extreme version of this idea. They physically output text rather than drawing pixels, so displaying images isn't really possible without replacing the hardware.