Eros and Agape are much more specific words than the English word love. Why was the word love decided to be the word for love? What are the etymological roots of love? Why did the English word for love not evolve to be as precise as the greek words?

Critical insight with the four-way classification of love in Koine Greek (Greek words for love): do not assume that the Greek classification was that clear cut. These are theologically useful idealisations. Like I already pointed out in Nick Nicholas’ answer to Why isn’t there a non religious equivalent of agape love?, the Diccionario Griego–Español’s definitions of agapē are:

1. Sexual love, with a link to Song of Songs thank you very much. (Inb4 “no, no, there’s no sex in the Song of Songs, it’s all metaphor.)
2. General sense: love, affection
3. Religious sense: love between god and humanity; Christian love, charity
4. a favour; alms
5. agape, communal feast; funeral feast; church, community

English certainly makes a distinction between erōs and agapē, without using the word “sex”: it’s the distinction between love and “being in love”. Modern Greek speakers would translate storgē as “caring” for a child, and would just as readily speak of agapē for a child. And while Aristotle defined philia carefully as a kind of love-as-loyalty, in ancient usage it overlaps with storgē, and lovers can feel it too (hence the –philia words in English.)