You identify two different sorts of rewards - the "rush" of getting it; and the "more interesting adventures" that it lets you partake in.In a certain style of play - challenge-based player-driven play - they are rewards for the player.
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If you get it, then your PC has capabilities that you otherwise wouldn't have. You could always just pass it by, though. But what a rush if you can get it! Now that you have it - what are you going to do with it?
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If the DM is determining the challenge or risk that you face, yes, things are easier and potentially less interesting. If you are able to grab that flame tongue in a player-driven game, though, maybe you think you can now sally forth into the troll marshes and set yourself up as their new god-on-earth.
I think these rewards are for smart play - you can now punch above your weight - so you take on more dangerous and interesting challenges
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the real reward isn't the flame tongue or vorpal weapon or crystal ball - it's the adventures that those magic items allow you to get into; more interesting adventures that you wouldn't be involved in if you weren't such a good player.
The first makes a lot of sense to me. And there are a range of ways of supporting that aspect of game play, of which looting items is only one (and often not the main one, because in traditional D&D play most magic items aren't obtained in the way you describe in your example, but rather by opening treasure chests after the rush of victory).
The second I am increasingly finding puzzling. As you describe them, the adventures sound interesting. But to the extent that the interest is a story/dramatic interest, it's not clear why that should wait on the players finding the item - why not get into an interesting story anyway (whether player driven or GM driven)? And once you set yourself up as the god-on-earth of the trolls, what happens? That seems like it's the end of the game, but D&D traditionally hasn't done that well with end-games.
To the extent that the greater degree of interest is a tactical/mechanical interest, I can see that, and I can see the logic of linking that to game play - that looks like a classic cycle of improving play in any sort of competitive game. It's also an argument for magic items that are more about breadth than simply bigger numbers.