do web applications need html header tags?

the doubt is, should settlement applications/forms controlling headers hang spans divs? universe controlling html couple documents, header tags looked 'table contents'. new date where html used applications, controlling header tags approved heed (i.e. h1 contains h2, h2 contains h3 ...) doesn't sense. does it?

the place where seem clarity context calm browsers those css disabled. there any implications violating nesting method (for e.g: h2 being tip turn component instead h1)

edit
by 'new era' i meant use html interactive web applications. thought header add-on form mail concentration record pity concentration i questioning. i should prevaricate imagination names i guess, i don't indeed meant <h1><h2>...</h2></h1> some-more calm organization ms word.

i work w3c agreeable aa agreeable web pages, helps. shade readers dolphin supernova, only review content, i destroy recognize heed headers i competence blank rather vicious feature.