So what are your thoughts? Is it a good thing to show that the password was changed lately?
Yes. Changing the system to aid people to sell accounts is not a good idea, nor is selling accounts in the first place.
I agree that its not a good idea but it happens and it would even happen when it would not be allowed. I dont think its good because it is used to scam, at least trying. Though nowadays there is a valid reason with the signature campaigns.
For example instead of saying an account was registered in June 2013, has 252 activity and 1300 posts, a seller can say that the account was created on or before August 2013 (or in the first half of 2013), has 250+ activity and 1,000+ posts.
I know what you mean but it seems that doesnt help in practice in my experience.