Computer displays can be read remotely by their RF emissions. At least it was possible with CRT displays. Not sure if LCD displays have this characteristic.
There is immense amount of work on audio, possibly coming from the need to discover and identify submarines.
It is easier to tell what a typist is typing from their audio signature than it is to TEMPEST a monitor, especially now with modern EMC requirements cutting down the usable signal.
Some people used to have "low emission fonts"; fuzzy edges in very low contrast.
The electrical emanations from the typewriter can be used to detect the characters typed regardless of whether or not an electronic display is used, and TEMPEST, which is a method of securing electronic devices, will protect the typewriter's emanations from outside detection, and, as mentioned by Daniel_Newby, electric typewriters are vulnerable to power line reading, but if the system is entirely disconnected from any external power source, as TEMPEST dictates, and the entire facility is held to TEMPEST standards, then the typewriter will be secured against external eavesdropping.
Any attempts at picking up audio|electronic emanations will be foiled by traditional TEMPEST type protection.
Typewriter ribbons can be dealt with by old fashioned incineration.
The only way to acquire a signal would be by infiltration of the facility housing the targeted systems.
IIRC researches were able to remotely read a laptop display. However, it seems like it would be much easier to build a large faraday cage than it would be to switch to typewriters.
Typewriters are trivial to fingerprint. All of them have slight imperfections in characters, spacing, alignment.
A cloth ribbon would be hard to extract anything from, I'd think, maybe you could with a brand new one. Carbon film ribbons as used in the Selectric yes, you can easily read them but they can be shredded or burned to dispose of them securely.