Why holograms in Discovery, but none during the TOS era?

This is an attempt at an in-universe explanation, also written as a reply under a video.

Shutting holographic communication down could have been to prevent leaks (during the Klingon-Federation War), but also to allow for increased verification of a person's identity in DS9, because it was very simple to forge transmitted imagery to appear as something else.

Other reasons for not including holograms would simply be long distance and increased communications.

In the first case, a 2D picture takes less resources to encode and compress, while a holographic image can be quite bandwidth-intensive.

In the second case, the volume (amount) of communications increased to such a level, that it became impractical to permit holographic data transmission at the expense of more 2D or plain radio contact that might have been of greater importance.

After the Klingon-Federation War, many of the base stations that would have otherwise supported holographic communications, must have been destroyed by the Klingons, while existing comms antennas were unable to handle such a traffic load.

Rebuilding that network would have taken a very long time, given, that the Klingons almost got to Earth, and on presumption, that they destroyed almost everything else.

Yet another reason could be loss of knowhow and production facilities during the war, making it impossible to create new kit on a mass scale that would have supported holographic communications.

There's also the trick of looking less advanced on purpose in order to misguide potential enemies as to the level of technology a Federation starship really possesses.