The visit wasn't formally necessary, no, but it was emotionally and psychologically necessary: in case House didn't respond as hoped to the job, in case this was actually goodbye, it was important to Chase to acknowledge what he'd been given; to acknowledge that House had played a significant role in shaping him, personally as well as professionally.
And as a teacher-in-training myself, I agree absolutely with what you've said: that's a debt that's repaid only when student becomes teacher, and it's the best teachers who instill the desire to teach in their students. (That's where I see Chase's character arc going, ultimately: that when House retires, he'll be the one who takes students and passes on what House taught. Because that knowledge shouldn't end with House's career, and Chase--by my reading, at least--would make a fine teacher in his own right.)
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The visit wasn't formally necessary, no, but it was emotionally and psychologically necessary: in case House didn't respond as hoped to the job, in case this was actually goodbye, it was important to Chase to acknowledge what he'd been given; to acknowledge that House had played a significant role in shaping him, personally as well as professionally.
And as a teacher-in-training myself, I agree absolutely with what you've said: that's a debt that's repaid only when student becomes teacher, and it's the best teachers who instill the desire to teach in their students. (That's where I see Chase's character arc going, ultimately: that when House retires, he'll be the one who takes students and passes on what House taught. Because that knowledge shouldn't end with House's career, and Chase--by my reading, at least--would make a fine teacher in his own right.)