I know that many, if not all, differential expression analyses of RNA seq data assume that the majority of genes are not changing expression. However, what if you have data that when a FDR cutoff of 0.05 is used there are 30%, 40% or even 50% of genes are differentially expressed ? What distortions in the results would be expected ?

Does it make any difference if there are only 5 conditions where this is so, but the analysis (DESeq2) was done with a total of 30 conditions (60 HTSeq files, or 30 with duplicates).