That's some interesting calculus there. You don't want to wash 2 cups for a total time investment of 60 seconds, so you choose to generate extraordinary waste to save 30 seconds, damage the environment and your health. Makes complete sense to me.
Not to mention if you're using the cup for only water and you're the only user then you can easily get away with washing it once a week or less. Washing a water glass after every usage is extraordinarily wasteful.
My solution saves all 60 seconds. I just use my coffee cup for water and never wash it. I wish I was joking.
You can use your coffee cup for coffee and hardly wash it.