Should all RPGs have character advancement?

We all remember how fun it was to "go up a level" but sometimes it feels like every roleplaying game since (except, of course, those oriented towards one-shots and short adventures) has to have a character advancement scheme even when it doesn't make sense.

Has James Bond ever gone up a level? Sure, you can point to ways that he's gained something along the way, but usually, it's more like he's bought off weaknesses or gained advantages, like favors he is owed, or rank and prestige. Have his skills really changed notably? (Disregard how they've evolved with the duration of the time they've been making books and movies -- yes, the original Bond didn't know how to hack computers and the latest incarnations do, but that's changing times, not Bond gaining levels.)

Has Jack Bauer ever gone up a level? If anything, he seems a little more worn out each "day". And since I'm exploring the "J.B."s, how about Jason Bourne? He's bought off weaknesses, but is he a better fighter or spy than he used to be, other than that?

Even outside the modern suspense/action genres, there's not nearly as much of this as you'd think. There's a lot of trading off advantages and disadvantages, but generally, the skills a character starts with are the ones they always have. Does Indiana Jones get gradually better at two-fisted action?

Counterexamples can certainly be pointed out. Consider the Lord of the Rings series -- who in that doesn't go up a level by the end! Well, I'll tell you. More than you'd think. Legolas and Gimli don't really get better at anything by the end, apart from buying off their prejudice weaknesses, for instance. They get more prone to bragging (particularly in the movies) but that's about it.

What about Aragorn? At the start he's a reclusive ranger with a self confidence problem; at the end, he has reunited the tribes of men under his rule. But did he really gain any skills? He certainly bought off that self confidence issue weakness, but even at the start, he had all the swordsman skill, the tracking skill, the lore skill, etc. that he has at the end. His only apparent area of improvement is leadership, but it's arguable that this all amounts to buying off that weakness, letting him use the leadership skill he already had. After all, though we never see it in the books, really, he was a leader amongst the Rangers even before the books start.

Gandalf, surely, you protest. Well, sure, when he came back as Gandalf the White, he clearly went up a level. But I think this is a much bigger change than going up a level. It was a profound transformation. In RPG terms, Gandalf always made more sense as an NPC, but doubly so after he became Gandalf the White (in much the same way River Tam makes a lot more sense as an NPC).

Okay, what about the hobbits? Yes, I concede, they definitely gained levels. And this is where you're most likely to see the level-gaining phenomenon, over and over: when the character starts as a "zero-level", a non-adventurer, and becomes an adventurer during the course of the story. Over and over we see this in all adventure fiction. Usually, when a character starts as an everyman at the start of a story and ends up a respected adventurer, if there are sequels, they fall flat, and we like to forget about them. But usually, when they do work, the character who gained a level in the first story does not gain any more levels in subsequent stories.

Maybe the best counterexample I can think of is Ripley, but even there, she's mostly going through the same arc as Pippin. One can argue about when she makes the transition from zero-level everyman to first-level adventurer, but clearly by the end of the second movie, with her charging into danger with a BFG or working her mecha in "hand"-to-hand combat with a xenomorph, she's an adventurer. Does she really ever gain a level after that? (Perhaps she would have, if the subsequent movies had sucked less.)

I think roleplaying games, particularly those with a cinematic turn, should not be so hidebound on the ideas "you start as a fairly weak grunt" and "you gain levels from there". There's nothing wrong with those ideas, but there's nothing wrong with setting them aside in the many cases where they really don't work. If there must be an advancement system, perhaps it should focus more on things like gaining favors owed, contacts earned, and weaknesses overcome.