It didn't start that way. In fact, there's a distinct correlation to the increasing age of George Lucas and the increasing "hijinks" of his characters and/or the ephemeral nature of the characters he introduces. JarJar is just the cataclysmic conclusion of a string of bad decisions that had a truly promising start.
In order, ep. 4 has witty repartee between Threepio and Artoo, somewhat diluted by SE retcons. This is the par excellence of their performances. You'll see that ep. 5 is where Threepio starts "hamming it up", but in a self-aware manner. A caricature of uptight British absurdism that doesn't take itself too seriously, played well as the "straight man" opposite of Artoo's escapades. Then in ep. 6, we get a par performance from Threepio with somewhat more heroic notions from Artoo. In a way, the Ewoks took the burden from the droid duo for providing the comedy/tragedy aspects of the third film. For the droids, those performances worked well enough and didn't take away from the story.
It all goes to shit with the prequels. Artoo is immediately framed as a "tragic hero" in ep. 1 because of the apparent slavery/fodder undertones of Astromech Droids overall. Thereby delivering a heavy-handed message of oppression and strife, "humanizing" this artificial-life character. Threepio, as the invention of young Anakin, is supposedly imbued with the values and morals of young Anakin, but doesn't explain how Threepio is unique from the protocol droids have been mass-produced for millennia. It's like building a toaster out of Erector/Technix parts... what was the point, exactly? Oh, right... it's a conveniently close-knit origin story that way. This film does little more than get principal franchise characters (Anakin, Obi Wan, Artoo, Threepio and Yoda) together by the end of the story. JarJar is introduced. He's inserted into the story as both a "CGI triumph" and as the sad clown. (I. Hate. Clowns.) In a way, it was JarJar that pushed Threepio into the "uptight ninny" niche that ultimately doomed him as a character and prevented any kind of humorous moments from Artoo throughout the prequel films. JarJar took over that job... kind of appropriate, considering the outsourcing epidemic that was happening at the time.
Then we get to the travesty of ep. 2; the Republic Army of Clones. (they didn't "attack" anyone, really... and it's a clear evasion of the obvious "Clone Wars" title, which would have made tons of sense based on canon, but was "strategically reserved" for a later animated television series.) If you can somehow manage to keep your last meal down and endure the frigid romance of Padme and Anakin for at least an hour, you'll see that the relatively minimal screen-time with the droids has been "lubed up" with predictable, over-the-top and depressingly corny gags. These two characters are ruined for being made into even shallower caricatures of themselves. There are zero moments with Artoo and Threepio that had to be written that way for the sake of storyline. Zero. Their abominable performances in this film were entirely by choice, and it was a very, very poor choice indeed. JarJar didn't even make up for it, he's now just a piece of the background. There's nothing less satisfying than to see a pathetic comedy-relief character turn into bland scenery. There's no real dichotomy here; JarJar doesn't offset Threepio in any way. And at this point, neither does Artoo. It's all ruined.
Now there's that lingering aftertaste; ep. 3. It's almost embarrassing to think of it, but it's the latest SW franchise feature-length motion picture to date. (*shudder*) While it has a most heroic opening, (Artoo... yes, again) this story later unfolds with almost no droids at all, and doesn't even really leverage them for comic relief. This was like putting ep. 5 after ep. 6 -- giving us a dark finish to a hopeful segway. The visual-gag moments we're given with Artoo and Threepio only reinforce the two-dimensional cutouts we laboriously endured in ep. 2. Nothing new to see here. JarJar is all but missing... but unfortunately, we see that he's still alive and doing rather well for himself; again, thoroughly unsatisfying.
If I were to visualize this progression, it would follow the chronological timeline of motion picture releases. (4 > 5 > 6, then 1 > 2 > 3) Under ep. 4, you would see the iconic image of Artoo and Threepio from the final "commencement" ceremony of ANH. (shiny and presentable) As you move to the end of the first trilogy, you would see them become more like drawn caricatures (anyone remember that animated "Droids" that assaulted us for a few Saturdays back in the '80s? Yeah, a bit like that) As we move into the prequel trilogy, we would see the stripped-down "naked" Threepio alongside a burnt-out Artoo, and as if Anakin himself had drawn it. In the second film, we see Threepio with plating (finally) but also amateurly hand-drawn... perhaps JarJar is trying his hand at it? (kinda like how Dub-yah tries his hand at painting) By the sixth film, the images of Threepio, Artoo and JarJar are just hand-drawn by a toddler, who is the only member of the audience impressed by their performances.
Thanks for the legacy, Mr. Lucas. May we please do it the right way now?