I completely agree with your first two paragraphs. (I may agree with your third, except that I haven't run across fics depicting their relationship as "Matt thinks how Stick treated him was okay and will do anything to get Stick to love him again" set during the episode "Stick.")
Whether Stick is disgusted by or interested in little Matt's attempts to bond, he'll react in exactly the same way, because he views relationships as inherently distracting and weakening. And he has managed to pass that lesson on to Matt, just as he passed on the lessons about using the senses and meditating and fighting. So I think the important thing about Stick's relationship with Matt is what he tells Karen in "The Ones We Leave Behind": "[Stick] has a way of, uh... getting in your head, you know?" His dad was the man who taught him not to fight, who shaped Matt Murdock, Attorney at Law; this is the man who taught him how to fight, who was instrumental in creating Daredevil. He's not quite so easy to dismiss as Matt wants him to be.
I'm not saying Matt is eager to win Stick's love in the episode "Stick," but I am saying that it probably took Matt a lot of time and a lot of years to be able to see Stick as clearly as he does there, and even then he still agrees to help Stick; I can see him as still hoping for his approval somehow here, or as him just reacting to a threat to the city he's trying to protect. I definitely don't have any issue with writers who want to expand on "Yeah, I've learned a lot since you've been gone," and that's where I've hit the stories where Matt initially assumes that how Stick treated him was fine.
Re: Does Stick actually care about Matt?
Whether Stick is disgusted by or interested in little Matt's attempts to bond, he'll react in exactly the same way, because he views relationships as inherently distracting and weakening. And he has managed to pass that lesson on to Matt, just as he passed on the lessons about using the senses and meditating and fighting. So I think the important thing about Stick's relationship with Matt is what he tells Karen in "The Ones We Leave Behind": "[Stick] has a way of, uh... getting in your head, you know?" His dad was the man who taught him not to fight, who shaped Matt Murdock, Attorney at Law; this is the man who taught him how to fight, who was instrumental in creating Daredevil. He's not quite so easy to dismiss as Matt wants him to be.
I'm not saying Matt is eager to win Stick's love in the episode "Stick," but I am saying that it probably took Matt a lot of time and a lot of years to be able to see Stick as clearly as he does there, and even then he still agrees to help Stick; I can see him as still hoping for his approval somehow here, or as him just reacting to a threat to the city he's trying to protect. I definitely don't have any issue with writers who want to expand on "Yeah, I've learned a lot since you've been gone," and that's where I've hit the stories where Matt initially assumes that how Stick treated him was fine.