"Washing" yeast is generally done by using an acid wash, etc. Rinsing it with water is sometimes done, but it really doesn't help the vitality of the yeast.
What I do is rack the beer into the keg, then pour the trub into sanitized glass jars. A pint jar full of thick yeast is enough for an 11 gallon batch the next time. And usually I get at least four pint jars after fermentation. So yes, saving the yeast is definitely worth it for me.
I buy yeast about twice per year, spring and fall, and usually 2 or 3 strains. From one $8 pack, I can use it once in a 5 gallon batch (and a different strain in the other 5 gallons and then save that one too), and then use it in an 11 gallon batch, etc- for about 3 generations before I just have too much yeast in my fridge. I probably spend about $40 a year on yeast, or less. And I don't have to make starters since a pint jar is enough for 11 gallons.