True, washes can be made well using just cold tap water for B&W prints and even film.
But, where speed and efficiency are important factors it is best to use a washwater, at least the temp. of the developer for film and about five degrees warmer than the developer for supports, soft water will help considerably with a wash agent added.
This is particularly important where the support is heavy grade fibre based.
The reason is that: the warmer the wash, the more the pores of the sport will open to allow efficient dishcharge of chemicals, and even quicker with a rinse agent.
It can be likened to us having a bath, where warm soft water will act more quickly on the pores of the skin, and even quicker with soap.
But then you already knew that.....