Something players and Trophy fans in particular love is sharing their Trophies with others. There are many online communities and tools built for players wanting to showcase their accolades and discuss the games they are trying to complete. It's a fun metagame in itself and a good way to meet people with similar interests.
Player profiles have taken a backseat in recent generations. On Steam they offer an incredible amount of customizations for a player to express themselves. This even has monetary benefits to the platform via the Wishlist feature.
Ideally a profile should allow for a Player to display up to 8 of their chosen Trophies along with favorite games, a background theme, quote, shared screenshots and clips. Being able to join communities and see the profiles of friends helps foster connections and shared interests.
I would argue that the current focus on being able to upload content to Twitter/YouTube/Discord is misguided. This is good for content creators with followings or people wanting to build an archive - but people don't want their gaming sphere to interject with their social platforms. People would rather have a Playstation page that they can compartmentalize their Playstation friends on, for example. This would be a more organic approach to integrating Social Media compared to the brute force attempts currently in place.