Sita parityag.

To know this incident we will have to understand the Kul of Shri Ram .

After dhobi incident, When public rumour spread of Maa sita, Bhagwan Shri Ram took the decision of Sita Parityag. 1/n

Even after that he consulted among his brothers and ministers about his decision , if someone had any other thought.
(Reminder - His council had right to spoke freely their thoughts even if he spoke any thing wrong).

For The dynasty of Shri Ram यश was the highest concern that whatever might happen but the कीर्ति of their kul ,their ancestors, their feat should never get maligned.
By Sita tyag the allegation that was put not only Shri Ram but also Maa Sita was to be removed.

Bhagwan Ram's was goal to make both Maa sita and His kul free from allegation.

Now you have to understand if Bhagwan Shri Ram wanted he could have said that this rumour was wrong, but would the common public believe the husband is giving clarification for his wife?

Or if his ministers did the same, public would refuse to believe a minister serving the King thinking it's just a government's propaganda.

After all this Sita ji accepted and laxman took her to Valmiki Ashram.

They could have sent her to Vasistha ashram or Bhardwaj ashram?

Note: Speciality of Valmiki Ashram - It was a self sufficient ashram ,free from any government interference and pressure . It did not take any,grant, subsidy or benefits from Kingdom and paid tax back to Kingdom. Fully आत्मनिर्भर.

So Valmiki ji was the most neutral person ever in the Kingdom in the eyes of public.
Valmiki ji taught Ram katha to Luv-Kush and sent them to Ayodhya during Yagya.

Even then they went to local streets to sing it , not to King's palace.
When common public started to here the Ram Katha (from Shri ram's birth to Sita Parityag) they asked who taught this Ram katha, there simple answer was Valmiki ji.

This cleared all the allegations against Maa sita as Valmiki was free from Government interference and would speak only truth.
In the people's mind allegations on Maa Sita was removed forever, that was the only goal of Bhagwan Shri Ram.

Otherwise Rakshas people in today's world would still question Maa sita.
They were Gods they did their Lila to teach people how to live for glory and righteousness.
We can see such degenerates today.