Because the E string is steel, has high tension, and is the least flexible string of all. It's very difficult to tune the E string with solely the peg because the slightest little movement changes the pitch more than the same amount of movement on other strings.
If you use steel core strings on your instrument it's not a bad idea to have fine tuners on every string. However, your sound quality and intonation could suffer.
When using synthetic core strings the fine tuners don't really have enough play in them to use them. Zoning in on the correct pitch (with synthetic core strings) is easy enough using pegs with the right technique. Also, longer string lengths (after length) result in a better sound.
Some decent tailpieces exist with built in fine tuners to compensate for the after length issue but the good wooden ones are not cheap.