* You get a video in a standard container and modern compression format you can host anywhere, and edit with video editing tools.
* Screen recorders can capture the microphone too, so you can explain what you're doing.
* Importantly, they can also capture the mouse cursor, which is useful even in a demo of a TTY app that has no built-in mouse support, because you can point to things in the terminal and highlight them as you speak. Mouse-based copy and paste actions are easier for the viewer to follow when there is a cursor.
* Everything you see is captured, pixel for pixel (other than very very fast, fleeting actions that are quicker than the frame rate, obviously).
* If in the demo you need to scroll up through the TTY history with the scrollbar or Shift-PgUp, that is all nicely captured. Your scrollbar is included in the video.
I can't recommend asciinema becuase while the tools to record TTY sessions are free, the animated rendering is done by uploading to the website. There are ways to self-host asciicast, but that looks like a huge PITA compared to a video file you can send to someone as a mail mail attachment, drop into a Slack channel, or put into a shared file directory. I don't want to become a host to give someone a file.
I tried alternatives to asciicast like ttystudio; they are all a hassle compared to even the most basic screen recording app like kazaa on Ubuntu, and lose on all the above points. But at least some of the alternatives give you a GIF file you can put anywhere.
Some work by simulating an ANSI terminal internally, rendering it to pixels and taking snapshots of that state --- which is just a form of screen recording!
I would say it's fair to TTY specific recording an anti-pattern. It seems cool and everyone is doing it, until they slap themselves on the forehead one day.