Wanted to add that imo one of the most harmful facets of finger exercises for the improviser or composer is that you start to build muscle memory for things that have no musical meaning to you.
This was a very real rut I had to get out of (TBH not sure if I successfully have!) because I used to do various drills and scale/arpeggio work all day.
About 20 years ago I was playing with a great musician and teacher and I said “when I solo it just sounds like I’m running scales and arpeggios” and he said “I hear a lot of my students say that. Then I ask them what they’ve been practicing, and they say ‘well…scales and arpeggios.’”
I know the following sounds dramatic but sometimes I wish I had never practiced scales as much as I did. In retrospect I think the way I did it really created distance between my melodic ears and what comes out on the guitar. (Knowing how to play scales and where the notes of every scale are is basically essential - being able to fluently blaze up and down the neck for every scale is a party trick or something cute for a video…)
Sorry for digressing as I know the topic is physically mechanical exercises, but similar principles apply IMO.
So, more specifically, I agree with @Tom_Gilroy 's premise here - I’ve sometimes had students be almost insistent that either I give them ‘general’ exercises, and/or that they have them as part of their practice routine, and it’s often been a hard sell that I want them to work on things that are much more specific to their goals and current strengths and weaknesses. Honestly I think part of it is just wanting something kind of mindless to sit and do to feel productive and to be able to say “I practiced.”
This isn’t a knock against any specific exercise, just the concept of ‘general’ exercises that aren’t trying to solve a musical problem. I give students tons of exercises, but I give them in response to whatever difficulty they are having with the actual thing we’re trying to play.