Is it necessary to use "Correct faulty and chopped off HTML"
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.