Why play by ear and improvise? Because music is an art.
‘And every music artist in the world, from Mozart to Justin Bieber and even Jay Chou, plays by ear.’
All other forms of art, dancing, literature, sculpture, or painting, require improvisation. For example, you do not dance with score sheets in front of you, right? The act of creation, spontaneity, is the very definition of art. Music as art and improvisation are inseparable.
Take language in comparison with music. To master any language, you have to learn to do four things: read, write, understand, and speak. Each has equal importance. But if you have to prioritise, which would be the most important or practical of all?

Speaking and understanding.

You should learn to speak the language of music, to communicate, and to improvise. Speaking equals improvising. Imagine that every time you are involved in casual conversations, you require scripts or score sheets in front of you.
‘We play by ear in everyday life because we just have to, whether for artistic or practical reasons.’