Quantile regression after classification

I am trying to predict the 10th, 30th, 50th, 70th and 90th quantiles of dependent variable. I have 110 independent variables in the data set. I can think of two approaches to do this.

1. Use all data points and then predict above quantiles using quantile regression.
2. First subset data into 5 groups i.e. [0-20], (20-40], (40-60],(60-80] and (80-100] and then predict median value for each group.

I am ultimately interested in coefficient values of independent variables at different quantiles.

With approach 1 - I mostly see either increasing or decreasing trend of coefficients from 10th quantile to 90 quantile.

I do not see such a trend with the second approach. However, what could be the potential pitfalls of second approach.