It's not only about showing off.
In my first levels, being able to see some other team's achievements was very helpful too.
For example when I had a friend request from someone, I was examining his profile.
If he had low level in "True fan", it was a reject from me.
If me and someone else were together in some auction, I was checking his "Mogul" lv or if he had the Stubborn achievement , to avoid a bidding war against him.
Of course now all those achievements has no meaning as I 've finished them (as all the teams of my lv) before many years.
But it would be interesting (if they are visible of course), to reset or to have some current achvm. for the recent - last 3 seasons for example.

Unfortunately the game goes more to visual than strategical development the last years.