I was thinking about why washing would be useful. I came up with the same conclusion, that it would minimize the amount of the source beer that works its way into the next. Being a nerdy scientist, I decided to work out the numbers to see how much actually makes it into the next beer. This is a thought exercise based on my equipment and methods. YMMV.
I don't have firm starting numbers, but assume I have 2 quarts of trub in the bottom of the primary. I add 1 gallon of sterilized water and swirl it around to make a slurry. The resulting suspension is now 33% the original trub.
I pour this into a sterile mason jar. I put it into the frige and let it settle out. Even though the solids have come out of suspension, the beer portion that came over remains in the liquid portion. When I decant the liquid portion, the source beer is now gone for all practical purposes. Let's say I now have 0.5 cups of the trub in my mason jar. This is mostly yeast, some proteins, hop junk, and any other misc ingredients in the boil. Percentages of each, I don't know, but I speculate it is mostly yeast, maybe 90% or more. Precipitated proteins the next greatest, say 9%, and hop junk the least, say 1% or less.
I now use this as my yeast in a new 5 gallon batch. The stuff I need to worry about contaminating my new beer are the 10% (proteins+hop junk) of the 0.5 cups, or 0.05 cups. This is 2.5 teaspoons. Doesn't matter if I make a starter, the amount of non-yeast components remain constant. 5 gals is 80 cups. I am adding 2.5 teaspoons of "contaminant" from the previous beer into 80 cups of wort.
The proteins have already left solution/suspension, so they shouldn't have any real effect on the new beer. Any flavor or aroma components in the hop junk portion have been exhausted.
Conclusion: I hypothesize the amount of non-yeast components in the new beer from the previous beer will not have an effect on the flavor or quality of the new beer.
Think I'll quit washing.