I move messages from my Gmail from SENT to INBOX and they go down on the list of emails because they don’t update for today’s date but keep an older date.
Exemplo: I have a previews email from 20/April. Today 22/04 I send an answer. Than I move this answer to INBOX. Instead of appearing as 22/04, it keeps on 20/April as the list of emails in the INBOX folder even having my 22/04 email there.
As normally we want to work the emails we just send we expect to see them in the top of the list, not lost in the middle
While there is no reason to move messages from Sent to Inbox, they will of course keep their sent date.
But what I think is confusing you is the Conversation mode. You can disable that in Menu > View > Conversations, and you should see the sent messages in their correct place.
It is always showing the latest message first. In the Inbox, it is in order of the latest received. In the Sent folder, it is in the order of latest sent.