That's what you should do if your intention is SEO. If you want to become famous article writer that's different story.
For SEO you are after quality backlinks.I would not say submit to as many sites as possible, what you should do is make a list of high ranked do follow article submission site and submit your articles there.
Submitting the same article to different article directories might be not acceptable on hot directories and would also have negative impacts for indexing purpose. Different original or spinned article submission would always be recommended.
Well i think there is no harm in submitting the same article on different directories as it will increase the visibility of your article and most people will be able to get the information you want to convey!