Is it necessary to use "Correct faulty and chopped off HTML" I'm allowing the users of the site to add comments in "filtered html" form.
And the input is in NicEdit though Wysiwyg.

Currently I'm using "Correct faulty and chopped off HTML" option in admin/config/content/formats/filtered_html

Is it still necessary for my site?

I feel it's an overhead!
It is not required when you are using the NicEdit though Wysiwyg.  Because, you are not using any tags in them. I you are concern to use the tags. Then, It is better to use this option. It will auto-complete and correct the faulty tags. 

for example : if you forget to use the closing tags. It will add those tags.