Some of this was probably deliberate; the show depicted computer consoles with ancient purely-mechanical typewriters. But still, I interpret the tagline "Twenty minutes into the future" as something of a disclaimer.
And, as you note, video phones were pretty universally envisioned as landline plus screen. As with many things, video has of course evolved much more organically. Initially primarily on mobile and, of course, it's exploded on notebooks/desktops in the current situation.
Behold, the Luma Telecom Video Telephone:
Looks like a press release from 1986: https://www.upi.com/Archives/1986/04/22/Luma-Telecom-Inc-has...
If you wanted some pics: https://www.worthpoint.com/worthopedia/vintage-mitsubishi-lu...
Romeo and Juliet (Juliet can't tell Romeo she has faked her death)
Assault on Precinct 13 (rioters cut phonelines to a besieged police station)
The opening credits for Terry and June [0] (they are looking for each other in the same shopping centre)