Three bytes are enough to fit nearly any of the chars in use in any language, including Chinese and Japanese
With only 3 bytes you'll completely miss plane 2, the "Supplementary Ideographic Plane" which includes tons of Chinese-Japanese-Korean Han characters.
I wish people would stop saying the supplementary characters are just for "emoji". Asian unification was very controversial and ultimately unsuccessful. Plane 1 and Plane 2 are important, especially if you're going to sell software or products in China or Japan where they are mandated.