Ram is respected because he is Maryada purushottam (maryada ki raksha karne wala purushon mein uttam …just a higher order of Krishna who is Leela purushottam).
Ram never asked Sita for agnipariksha. The kingdom asked Ram whether she deserves to be the queen after being abducted by a Rakshasha king. Ram had complete Faith over Sita’s chastity..
Rama preserved his Dharma both in the jungle and the forest. He gave up his comfortable life for his father, went on to jungle to fight daemons and then assembled an army to rescue his wife. Later he let go of that wife to preserve his Dharma as a king.
Hence you see, misery in the palace and misery in the forest. For Dharma and righteousness. Hence Rama is worshipped because he knows when to let go.
Ravana is not worshipped since he is that alpha male who doesn’t care.
“Your wife is my wife. I will grab it by force”
” I will not let go of that little toy even if the kingdom is burned”.
Ravana doesn’t know when to let go. He acquires for personal ambitions, lust, desires and his kingdom suffers because of his personal greed. This is unworthy of a king and hence he is not worshiped.