I'm 55, and I can confirm that this was definitely not a thing when I was was playing (pre-teen up until 23 or so). Literally never saw it, never heard of it (honestly had to google the term when I first read it, as I was completely away from tennis for 30 years). Warm up basically consisted of some static stretches and maybe a 5-10 minute run, then starting with some light hitting from the baseline. If a wall was available, I would always warm up with that.
I like the concept as a warm-up though, and as I'm instructing my wife, who is new to the game, I actually think it's a great way to warm up--mostly to get re-acclimated to the distance between the hand and the ball. I also think it just helps get the brain warmed up with ball recognition. Lastly, it helps with half-volleys, something a lot of folks rarely practice.
FWIW, I use my volley grips, basically an Aussie forehand/conti backhand. As far as "warming up" to prevent injury, I have another strategy though: I just don't run after balls for the first 5-10 minutes or so. You don't need mini tennis for this. Just don't pretend you're Rafa for the first few minutes and ease into it.