I was just replaying Red Faction Armageddon in New Game + mode that let's me keep all my weapons and upgrades. In the game you collect scrap which you use to buy upgrades. At this point, I've purchased everything in the game.

Why then do I feel the urge / compulsion to collect more scrap? There's no rational reason to pick it up any more since I can't buy anything else, but I find myself doing it anyway.

Why do I feel compelled to collect something I can't even use?

It's not just in games. I do it in my life too. I'm not a hoarder, but I do definitely collect things.

Is it some sort of instinct? Does anyone else feel the same way?

It's indeed an hoarding instinct, even if it's digital.
I guess it's for the safety feeling it grants? You (we) accumulate "just in case".
It's also somewhat of a delusion of immortality XD
I guess it's not a big deal unless it redirects too much time & money from something more important.

I'm more the sort of person who doesn't like to ever get rid of unique items.

For example, in Wizardry 8, I'll hold on to all those instruments or gadgets, or at least put them somewhere safe, even if I'm not using any Bards or Gadgeteers in the party.

Or there's cases like (original) SaGa 2's Revenge sword. It's not particularly useful, and there's a buyable item that does the same thing, but there's only one of this sword, and no way to get more. (SaGa 1 also has this item.)

It does get annoying when there's limited inventory space and no place to store items. That's a problem in SaGa 1/2/3 (though remakes of 2 and 3 added places to store items), as well as Final Fantasy 1 and 2 (though remakes added unlimited inventory space).
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I could also say it extends to unique consumables, including things like Megalixirs and even Dragon Quest 3's Book of Satori (in that last case, the item's use can be avoided by going through Goof-Off/Jester, which will allow changing to Sage without the book).

Probably a leftover from our past as "hunter-gatherers".

Yeah natural instinct, not just apes do it either.
Think of the fox in the henhouse, they'll kill all the chickens even though they end up eating only one.

If I may be allowed a very cynical take on all this, collections belong in a museum. It's either that or they'll eventually up in a trash pit once their collector is no longer around. I've seen it happen.

Digital collections at least don't take up garbage pit space, so are less of a polluting factor. +1 to us game hoarders.

In new game + i collect only what i really need, but if a game don't let me keep what i got from previous save, i recollect everything if there is not a lot to collect unless you can buy a map that display everything.

Probably the instinct of "just in case." I think every JRPG would knows the feeling of not wanting to use rare or limited items, especially if they cant be farmed like in the video below.

https://www.youtube.com/watch?v=rgU4Oum8SLg

There is also the curiosity of what happens when you hit the cap. Does something unlock? Does a glitch occur? What exactly is the cap? After making collecting scrap or items part of your "routine," its hard to break the habit.

The behavior you're describing, where you feel compelled to collect or gather resources even when they no longer serve a practical purpose, can be attributed to a combination of psychological factors:

1. Conditioning and Habituation: Through the course of playing the game, you've developed a habit of collecting scrap. This behavior has become ingrained in your routine, and your brain's reward system is still activated when you collect scrap, even though the practical need for it is gone.

2. Completionist Tendency: Many individuals have a natural inclination to complete tasks or collect items even if there's no functional benefit. It's the desire to "finish" or "perfect" something, which can trigger feelings of accomplishment and satisfaction.

3. Psychological Reinforcement: Collecting scrap may have initially provided a sense of achievement and gratification. These positive feelings become associated with the act of collecting, creating a cycle where you continue to seek those positive emotions, regardless of the actual utility.

4. Sense of Control: Collecting things can give a sense of control and order in both games and real life. It's a way of asserting agency over a situation or environment, which can be comforting and reduce anxiety.

5. Neurological Factors: The brain's reward centers, such as the dopamine system, can play a role. The anticipation of rewards, even if they're no longer necessary, can still trigger the release of dopamine and the associated pleasurable sensations.

Many people can relate to this feeling in various contexts, not just in gaming. For instance, people might continue to accumulate items or engage in certain behaviors because they've become accustomed to them or because it provide a sense of security. If this behavior starts to interfere with your daily life or cause distress, it might be helpful to explore it further with a mental health professional who can provide tailored guidance based on your specific situation.

Not just JRPGs. I remember I finished Fallout 3 with some insane amount of weapons, ammo and other gear I was hoarding for the final fight... only to discover the game doesn't really have one. I was so angry, thinking of all the enemies I could have straight up nuked throughout the game...

There's also a couple other factors at play, at least when it comes to consumables (particularly on a 1st playthrough):
* The player doesn't know how much of the game is left. There are many RPGs where you reach what looks like it should be the final boss, only for the game to not end afterwords.
* CRPGs (including JRPGs) are notoriously bad at sustaining difficulty. When a player reaches a difficult fight, a first time player is thinking something like "if it's this hard *now*, it's going to get unreasonable later, and I should save my items for then", but that "later" never actually comes, and the game gets so easy that those consumables have no usage. (This strategy works better when the game difficulty increases, or at least sustains itself, through the end, but that's not what usually happens.)

Assuming it is not obsessive, it is normal to feel a sense of gratification when looking forward to something. Some folks collect things as a "hunting" instinct. Seemingly random things found, is like a treasure hunt.

As to collecting after one has everything they could get? Well, the journey may end, but the instinct does not. Just stop when it become unhealthy. That is subjective.

When in doubt, follow RPG logic and pick up everything. - Ghost 1.0

For your sake I hope you avoid playing Subnautica. All those resources you can harvest and hoard!