Improv is one of the most transferable skills you can learn. No matter who you are, or what you do, there will always be things which happen outside of your control. For some people, being able to react in the moment comes more naturally than others, but it's a skill that we can all develop.
When most people think of improv in music, they think of jazz. Highly skilled musicians making it up as they go along. In fact, improv is intrinsic to all genres of music. How does someone write a song? You start with an idea. That idea comes from your imagination, it's an accumulation of all of your conscious and subconscious thoughts coming together in that moment to create something new. Once you have that idea, you need to find other ideas to go with it. You try some things which work, you try others which do not, you persevere. Slowly you build up these pieces, to make something whole. Whether you're working alone or in collaboration with others this is unavoidable.
It may surprise you to learn, but many classically trained musicians don't have this skill. A beautiful recreation of an existing classical music piece requires no improvisation. If anything it requires anything but. Someone could be capable of recreating the most beautiful tunes ever created for their instrument without missing a note, but if you told them to "jam in C major" they wouldn't know where to begin. It doesn't diminish their capabilities, but it limits what they can do, and who wants to be limited in anything that they do?
Collaborations with others expands your horizons, allows you to view things in new ways and bring fresh ideas and perspectives that can inspire something new in you. It can help you get out of a rut or stimulate you in ways that you may never have been before. Whoever you are and whatever you do, there are things that improv can do to put you in the moment, to listen to other players and be able to react and collaborate.
It's not just songwriting that's improved with improvisation. Every musician will perform live at some point, and every musician will experience something unexpected while doing so. Whether it's a technical problem, something with the audience or anything else that comes up unexpectedly, live performances are by their very nature prone to problems.
There was a great anecdote that I heard years back about a Cypress Hill performance at a major music festival. Everything was going great when suddenly the DJ was hit with a power cut. All of the music stopped, with only the mics left active. As it dawned on them what had happened, the crowd cheered in the schadenfreude of it all. Imagine the stress of that happening. In that moment, with thousands of inebriated people in front of them expecting music. It's not just about doing a good job, an amped-up festival crowd could get ugly fast. Until that point, they would have been operating on a relative autopilot, working their way through songs they've performed thousands of times before, but suddenly they weren't able to do what they'd planned to do. Rather than panicking or finding someone else to blame, after the few moments it took to work out what had happened, they just turned to the audience and said
"Everyone... WE FUCKED UP!"
It resulted in the biggest cheer for their entire set, prompting a chant of "YOU FUCKED UP" until the power came back and they picked up where they left off. In this moment where there was no right way to act, no script for what needed to be done. They turned a bad thing into something so memorable that someone who wasn't even there is recalling it years later.
Improv isn't just for one group of people, it can help us all. If you're not doing it, start. If you're doing it, carry on.