I wash mine at the end of each season. I've had my original wicks for several years. They only started to fray after about 3 years.
The "water proofing" effect also limits the amount of fuel they can absorb, in my experience. The soot builds up and acts as a barrier.
However, that is the only reason I do it. It doesn't stop anything from turning black. It doesn't take all of the soot off.
I've also accidentally left mine in the rain, in a bucket and had them soaked.
They dried out just fine without issue.
The whole "ruined by water" thing (as long as you aren't stopping bullets

) completely mythological.