The reason for washing is to remove the alcohol and other fermentation products, these can cause problems from two directionsI'm always curious as to why people bother to wash yeast. Why not just make a larger starter and harvest from that? A lot less messing around.
I crash cool, remove most of the starter beer, transfer to a smaller container to minimise headspace and store it in the fridge until it's time to make a new starter. I've got at least 10 uses out of one strain of yeast without any noticeable changes and that was left in the fridge for about 2-3 months before pitching into a new starter.
Saves me a heap of cash and time.
First Mutations are accelerated by contact with fermentation biproducts.
Second Reducing the osmotic pressure on the yeast helps to stop it loosing minerals water and other cellular products that it will need next time you use the yeast. Ideally use mineralised water (very similar to what's in the wort you will by using when you next ferment)
Acid washing is to reduce bacteria, by acidifying to around 2-2.2pH you can kill off most beer spoilage bacteria (if you think a multi generational culture contains just the yeast you want you seriously mistaken (probably)).
For short term storage (days) the risk of getting an infection by water washing probably increases the risk of infection just through handling and exposure to air, for longer term (weeks) storage water/acid washing has distinct and measurable benefits in terms of strain purity, contamination counts, yeast health...
For very long term storage (months+) you really need to be thinking about plates/slants/freezing... followed by stepwise re-culturing up to pitchable populations.