Can I aggregate all stylesheets core, contrib and custom into one single stylesheet? Is there any way to avoid Drupal from serving multiple stylesheets and instead bundle them together? I am going to look into https://www.drupal.org/project/webpack 

I want to avoid all the multiple @imports if possible that get created by the modules. Reason I want to do this is I am archiving my site with wget and I want to have less stylesheet links to monitor.
Enable aggregation of css by going to admin/config/development/performance

This is the best Drupal 7 can do without the need for any contrib module 

You can also try Advanced CSS/JS Aggregation which gives some more advanced aggregation.