Hence why you need to rinse thoroughly....... Which is also why the vessel can no longer be considered sterile.
Yeasties need a bit more protection to be sure, especially if any time is going to pass before re-use.
When I have a batch fermenting, the day before racking time (from the primary) I take one of my large flasks, boil 800ml of water in it for 15 minutes, cover it with foil, and let it cool. After racking the beer (which in my case is almost always to a secondary), I dump the now cooled water into the carboy with the yeast, mix it well, and dump it back into the flask.
Covered with foil (and a rubber band if one is handy) it lives in the fridge until I'm ready to use it for another ferment, generally within a couple weeks. I've found washing the yeast to be unnecessary, even with my habit of 8-9 repitches.
20+ years of doing it that way has only ever resulted in a lost crop twice (once due to a fridge malfunction, and once when I was on tour and waited too long to reuse it for another brew after I returned home).
Other than that, just keeping it simple and keeping it clean has served well.