In RNA-Seq analysis, why is it mathematically necessary to normalize raw read counts by both sequencing depth and gene length before comparing the expression levels of two different genes within the same sample?

Raw read counts from RNA-Seq are a measure of how many sequencing fragments were mapped to a specific gene, but these counts are inherently biased by two technical factors that must be corrected to make expression levels comparable. First, normalization by sequencing depth is required because different samples or sequencing runs produce different total numbers of reads. If you sequence a sample more deeply, every gene will appear to have more reads simply because there is more total data....