Why do NMR spectrums have the higher chem shift values closer to x-axis?
This convention stems from historical reasons only. In the early days of NMR, there were a number of different ways to report NMR data; values for 'shielding constants' of nuclei was of most interest, rather than what we commonly refer to as chemical shifts. The two most common scales were the tau and delta scales . The tau scale had the chemical shifts running in the opposite direction, with increasing shielding constants running from left to right. 

A third scale, the sigma scale was very commonly used, especially in heteronuclear analyses, and again had the shielding constant increasing to the right. This scale was favoured often by theorists, as it was usually a direct measurement of the shielding constant. 

A mixture of tau and delta values was regularly seen in the literature up until IUPAC made their initial recommendations, in 1970. This was to adopt the delta scale, and report chemical shift relative to TMS at delta 0ppm, as values of chemical shift, which are dimensionless and, hence, field independent.