Improvisation is a fantastic skill to improve. Even if you don't consider yourself spontaneous, or if you prefer to think deeply to acting in the moment, you should cultivate your ability to improvise.
The main reason to improve in this area is the cost advantage over planning. If you model the space of possible scenarios as slices in a pie chart, and the actual scenario as some point on the chart, then planning for every eventuality means thinking through every slice, even the never used ones, and paying whatever cost in time or in research that is associated with that slice. We can say that the cost is a function of the area of the slices, which in this case means that it's going to be expensive.
The cost of improvisation, on the other hand, is the cost of drawing a line from the center to the point, and it's much cheaper to draw a line (one-dimensional), even a squiggly line, than it is to fill in area (two-dimensional). If we think of your ability to improvise as the length of the line you can draw, then modest improvements to your ability to improvise can replace massive amounts of planning effort.
I would actually prefer to think of improvisational skill as the maximal number of steps of non-deterministic computation you can perform. Planning, then, means exhausting the full range of possibilities via deterministic computation. This is less accessible even than our line-segment versus area comparison, so I'm giving both.
If you were still arguing for planning, you might point out that many times you can narrow down the space of possible scenarios to a handful of possibilities. That's true. And in those cases exhaustive planning might be superior. But experience shows that scenarios we have not accounted for happen with regularity, and that, even when we've identified all possible scenarios, that it's infeasible to make plans for all of them, especially when you consider that in real life there are multiple charts on which to allocate your limited resources. The economics basically make exhaustive planning impossible, and even when it is possible, it's too expensive anyway.
This I think is the main communicable thrust of why improvisation works. There are other just-as-important but incommunicable benefits that come from improvisation, which I believe is due to the fact that improvisation sits in the middle of a related group of life skills.