Dear fellow Budoka,
I don't know where and how you train, but I do sweat a lot during class (when training and not teaching). I wash my belt (and hakama) once in a while for the same reason as Jorgen just explained.
On reason #3 - good lough! Thank you! If "my Ki" was in the belt, not only would I (have to) wear it all day, I would wear two of them! (Much like H.Ikeda Sensei's "power connectors" he pulled out of his Gi from in front of the lower abdomen, BUT he was joking!).
Happy training - and please wash your stuff once in a while!
P.S. Some Yudansha don't (have to) wash their black belts (or hakama) -- it's not because you don't see them sweating on the mat anymore, is it? (BAD REMARK...I know)