While the treatment of Anderson at the end was heartwarming, there's an element of practicality to his decision: four corruptible judges were killed in the course of the film. Given the high crime rate, and manpower spread thin, they need every possible good judge available, especially one who is not only a powerful psychic but more idealistic.
Dredd constantly asks Anderson questions about what to do next. This is not just explaining to the audience (because he's Dredd, of course he knows what to do next) - he's testing Anderson and asking her examination questions while they go about their business. He even evaluates her - there's a lovely scene after they break into a Slo-mo den and Dredd pop quizzes her on sentences and procedure after they've pacified the situation, and Dredd gives a tiny, almost imperceptible nod after she tells him the right answers.
Also notice that Dredd usually makes her walk in front — which makes sense because this is her evaluation, so he's keeping her in his field of vision so he can watch how she does. However, Dredd moves her back and takes point whenever they're breaching a door — which also makes sense, as when you're going into a room full of bad guys you want the first guy through the door to be the best marksman.
When Kay fantasises about shooting Anderson during a Battle in the Centre of the Mind, he's imagining himself using a Lawgiver. Guess he really did always want one of those...