They always make a point of how the Doctor doesn’t know what he looks like when he first regenerates. After all, how could he? Of course he’s gonna go running around blind for a while because regeneration usually happens when something important is going on, so he can’t check the moment it happens. He’s presented with an exact duplicate of himself and doesn’t have the faintest clue who it is because he’s been kept so busy since he gained the new body. Understandable. It works, both from a character perspective and on a meta level as well. The Doctor’s a bit too busy and distracted to go looking in a mirror two minutes after he regenerates and then we, as an audience get to see him react to his new appearance, usually with some self-deprecating comment or dashed hope on his part.
But when Mels regenerates into who we know as River Song, she goes out of her way, mission be damned, to get to know her new body and celebrate the new changes. But, more importantly, from a viewer’s perspective, Mels taking the time out to study herself, more than once, was essential to the plot of the story and even the lives of her and the Doctor.
When the Doctor is laying on the ground dying and she asks Amy and Rory who the mysterious and oh-so-important River Song is, the Tesselecta revealing her own image just wouldn’t have worked if she didn’t already KNOW what she now looked like and had taken the time to get to know and appreciate it a bit. Sure, Amy and Rory could have explained that she was River Song, but it wouldn’t have had the same effect - on the audience and definitely not on the character. She had to see her own face staring back at her in that moment to get that real moment of clarity she has at the end that spurs her into sacrificing her lives to save the man she just killed. Because that woman she was just shown may go by a different name but she has her face, and seeing that gave her the strength and motivation to break free from her brainwashing and make a decision for herself for the first time in her life and which in fact starts her on the journey of actually becoming River Song.