Water conducts heat. It is the same reason why you don't want to be wet in cold weather.
(The weight of the water is only a minor problem in comparison)
If you try lifting a hot pot in the kitchen with a dry and then a wet towel you will see why you want to be dry.

You don't want clothing that turns into fuel for a fire or that will melt and stick to your body either, but it is unlikely that people will start wearing Nomex everywhere all the time.
A lot of times people are severely burned because their clothes caught fire.