I am quite nervous about certain foods and reheating (seriously, if you'd ever been as ill as I was once with food poisoning, you'd be nervous too), but when I want something like egg fried rice in the evening I will cook the rice a few hours in advance and let it cool. I have never rinsed rice more than one or twice.
Also I don't get why you always want rice to be non-sticky, if I am eating something with a pair of chopsticks, I don't want all the starch washed out and every grain to sit alone and separate from its neighbour. Sometimes rice being a bit clumpy and/or sticky is desirable, depending upon how you are using it.
I use the absorption method for cooking rice (so I don't boil it!), and usually it being clumpy is due to too much water or insufficient 'fluffing' time (time after it is taken off the heat and stirred with a fork to separate grains then covered again off the heat for a few minutes).