Well, one reason is that because sometimes we are interested a quantile value of some measurement. Like when looking at income or home prices, we often look at the median value. Usually, when statistics are reported for e.g. "the average American", we are looking at the median value. We might be interested in other qualtiles as well.

Salvatore S. Mangiafico, thank you sir

The quantile regression coefficients often differ for each quantile, giving additional information not available in the linear regression. Check the second paragraph of the Introduction section: Article Application of Quantile Regression to Recent Genetic and -omic Studies