I recommend this to most people I have helped or tutored over the past years for a few reasons.
Problems are complicated when you don't understand them.
Basic problems are not as easily digestible to students, especially those who are less confident.
I have found people consistently make mistakes based on the problem definitions even if they are explicitly given and as a result I strongly recommend people to write them out. Even if it's repeating information.
This is true even for simple problems. As problems get more complicated this is even more important.
People don't read well.
I eventually tired of people making mistakes resulting from simply misreading or misinterpreting assumptions or even given information.
Forcing them to write this down at least somewhat helps, though, of course there's always opportunity for stupid mistakes.
It can be part of problem solving.
I can't count the number of times in the past I've had no clue how to approach a problem myself, but followed my normal approach of writing the problem down and as I was basically rewriting it, ended up with significant insight into how to solve the problem.
This is also the "if I write down lots of stuff it'll look like I tried" perspective, though, this is more "student led" than something I ever recommend..