Write it down because the process often helps me better think about the problem & reasons my initial assumptions were wrong. Can't tell you how many times my clever initial idea becomes terrible rather quickly.
Also if it's something that's going to exist over multiple days, writing it down & coming back to it at least a day later is a great way to re-approach the solution & idea.
Write it down to read it & not forget it.
Write it down because the process often helps me better think about the problem & reasons my initial assumptions were wrong. Can't tell you how many times my clever initial idea becomes terrible rather quickly.
Also if it's something that's going to exist over multiple days, writing it down & coming back to it at least a day later is a great way to re-approach the solution & idea.