Update. Hope this helps.
After looking more closely into multiBigwigSummary: read counts in each region are averaged over the number of bins. Meaning that the end score is dependent on the gene length. After normalizing gene counts from the original bam by length, now the correlation score is 0.95.
I agree that in most cases focusing on gene boundaries for getting BED scores is not the best approach. In Spombe yeast though, many genes are signle-exon which makes an acceptable "approximation" of expression. Of course, finding the exact expression values needs some workaround.