I'm a very strong believer in the interpretation of gene lists as being inherently non-automatable, as they must always be interpreted in the light of the biological quesiton that was being posed in the experiment, and the investigators pre-existing knowledge of the system being studied. However, I'd generally say that my process for extracting a full meaning from a gene list takes anywhere from weeks to months or even years.

But if I were to comment on the pipeline above, I'd say that your enrichment tool of choice is going to need to be chosen for the data type. Specifically standard enrichment tools are very unsuitable for GWAS hits: Longer genes are far more likely to contain mutations, and any analysis must take this into account. The same is true to a lesser extent for RNA-seq.

For RNA-seq I like either GOSeq, with the Enrichr library, or GSEA. I tend to use GSEA, or GAT for ChIP-seq, and GAT would also be appropriate for mutation based analyses I think, although there are specific tools.

The bottlenecks are always - sorting through the results and seperating the boringly expected, from the totally irrelevant, from the interesting, and reading the associated literature.