Sounds like things have changed in the search engine world in the 8 years since my website first went online.
Back then ... they suggested submitting your site no more than once a month ... and they only scanned meta tags.
Now depending on who you talk to ... they say you do not need to submit that the sites are scanned automatically. That they use a sites robot.txt instead of the meta tags ... and others say the search engines scan each page and build their databases on what their spiders send back.
My own experience ... depending on the search engine ... each one scans the site differently and Google seems to be the most effective. But I use meta tags, robot.txt and language in the first part of every page to make sure there can be no confusion of what each page is about. I figure that covers all the bases.
My suggestion ... if your site is real new then yes submit it to the search engines. If your site is established then chances are you are already in the loop for regular scans by the search engines. Read the tips & tricks on the various sites on how to improve your ranking in searches ... and implement them. And be patient.
I don't think I ever submitted my site to a search engine ... but I get 4000 to 6000 unique visitors each month. Not bad for a personal site