Interestingly, the only time in the entire series Tintin does anything that could be called reporting is in the very first story, Tintin in the Land of the Soviets. The beginning of the story firmly establishes him as a reporter for Le Petit Vingtième (the real-world children's companion to the catholic paper Le Vingtième Siecle) where the Tintin comics were published. In fact, the first panel sets up the idea that the stories are supposed to be a kind of "real news" written in a format for kids, so they could follow what's happening in the world. Tintin does some real journalistic legwork here: he exposes election fraud, catches on to some Soviet-style indoctrination, reveals some propaganda aimed at some foreigners, and even sits down and writes some stuff!

It would not last long, however. The two bottom panels in that last image is the only time in the entire run of comics that we see Tintin actually writing.

The next two stories (Tintin in the Congo and Tintin in America) sets up the story by saying that Tintin is out on assignment, but him being an actual reporter plays no real part. In Tintin in the Congo, we get a scene of a few different editors trying to outbid each other to get Tintin to write for them, which he refuses (given that he doesn't actually write anything in the story, you could say that they got of easy!). In Tintin in America, the notion of him being a reporter is basically in one panel of the story, and then dropped immediately.

(in case it isn't obvious from the images: Tintin in the Land of the Soviets and Tintin in the Congo are both god-awful and should only be read by people interested in the history of Tintin. Tintin in the Congo is especially heinous, containing many incredibly racist portraits of Africans, which has stirred some controversy in some countries about whether or not it should be in included children's libraries)

But that's as far as it goes with this conceit. In Cigars of the Pharaoh (the fourth story), Tintin is on holiday when the story starts and he just basically falls into it and the next one, Blue Lotus, is a sort-of sequel to Cigars to the Pharaoh. The one after that is The Broken Ear, which you mentioned. In that story, Tintin hears a radio-report of a robbery at a museum which he rushes to, meeting the Thompson twins there. No reason is given for why he rushes over there. I suppose he might be thinking of doing a story about the robbery, but it's never made explicit. He more or less just "falls into it", just like in Cigars. That would remain the pattern for the rest of the comic.

Because of his lack of writing it is sometimes joked that Tintin is the least hard working journalist with with the largest expense account in the world. But, Cigars of the Pharaoh actually provides us with a hint at what it is that Tintin actually does! In one scene, Tintin gets taken prisoner by a sheik, who, upon finding out his prisoner's identity, is absolutely delighted and has his servant bring in one of the actual Tintin comics. This would seem to imply that these things we're reading is not just the stories of Tintin-the-reporter retold in comic-book form, but that Tintin is the actual author and artist behind the stories as well (Hergé being his pen-name, presumably). It would explain a lot.

(I've always wondered about that panel by the way. I've never seen the original version of it, just this redrawn version. The comic the servant is holding is Destination: Moon, which is a much later comic than Cigars. By the time Cigars is published, Tintin hadn't even met Captain Haddock or Professor Calculus, who of course both play a big role in Tintins moon adventure. It's a fairly staggering blunder for a comic like this, and even at age 9 it really bothered me. I'm really curious what the servant is holding in the original. I'm presuming that it's a copy of Le Petit Vingtième, but I don't know for sure)

Anyway, after this, Tintin's occupation plays almost no role in the stories, except for the occasional character who says "Hey, that's Tintin, the famous Belgian reporter!" It should be said, however, that never stops being a reporter. Throughout the series, whenever his occupation is mentioned, it is always "reporter" and it is always in the present tense. It is mentioned even in the last finished album, Tintin and the Picaros.

So, to answer your question: Tintin is introduced to us as a reporter because the original idea for the feature was a sort-of kid-friendly "tour of the world" with your friend Tintin, with the illusion that he was an actual reporter working for Le Petit Vingtième, but that conceit is abandoned almost immediately and is basically gone by the third story. By that time, it's just becomes adventure tale starring Tintin. It is also around this time that Tintin starts taking shape and become the story we all recognize. The tone, writing and art are all cohering into Hergé's distinctive style, a process which more or less completes with Blue Lotus.

Also, The Petit Vingtième only lasted until 1940 (it was closed down by the Nazis), and during the war Tintin was published in Le Soir Jeunesse, the children's edition of the newspaper Le Soir, so he couldn't very well be a reporter for that publication any more. The stories published during the occupation are notably less political than what has come before (the last story published before the war was King Ottokar's Sceptre, which is a thinly veiled retelling of the Anschluss), and this is sometimes given as the reason why Tintin "stops being a reporter". That is not entirely accurate, however. Tintin's job stops being relevant long before this, and after the war (when Tintin gets it's own magazine) the stories become every bit as political again. Hergé never lost his edge, and Tintin never lost his press badge.

He was originally a reporter for Le Petit Vigntiemme which I believe was a real newspaper aimed at young people. His adventures were initially serialized in this paper as if they were dispatches from Tintin.

During WWII, in occupied Belgium, Herge continued to publish Tintin in Nazi controlled newspapers. As such, after the war he was seen as a sympathizer by some and he fell out of favor and his career was essentially over until a publisher effectively saved him by offering him creative control over a children's magazine through which he was as to continue Tintin's adventures.

As for why he stopped being a reporter, I believe it's referred to obtusely in a couple of the later volumes, but you're right that it's not the main drive of the books. I think Herge used it initially as a way to put forth anti-communist political ideas, but as time went on, his views changed to more altruistic ones and the framework of the reporter wasn't as overtly necessary as he deemed it in the beginning.