I like the implied premise of your first bullet, i.e. that we can hardly find the mechanics interesting if there are none. I feel like your fourth bullet is a subset of that - we find the mechanics interesting because they simulate something in a way we're interested in. So I would make your first bullet a 6th reason why RPGs need rules.
The middle two I feel fall well into - rules could do this, but are not necessitated. The group could just agree to enforce setting tropes on themselves, and similarly could just ad-lib some starting points. That doesn't mean it wouldn't be more successful with rules; I am drawing a line between what is necessary and what is ideal.
EDIT #3 can be PvP but isn't limited to PvP. Players can want their PvE play to be competitively robust. (They can also want their characters to be able to come into conflict without that amounting to antisocial play. I note your "seldom seen", but in some modes it's more common.)
Player agreement to some limit is still a rule, albeit a different tier of rules from explicit and implicit rules-as-written and written houserules. But for licensed games, genre enforcement is one of the primary selling points. Further, for many players, unless it's in rules text, it simply will not be agreed to. I've often encountered players unwilling to adhere to restrictions not in rules. (There are terms for such people... rules lawyers, munchkins, power-gamers all tend towards that.) Had one who so egregiously violated the group agreed (annd verbally agreed to by him) restriction in a GURPS game, an agreement that every character had the same patron and either a deep sense of duty to him or a weaker actual duty; said player rewrote his sheet after approval and tried to pass it off as the approved one. He decided to kill said patron... I reacted poorly, but everyone else cheered when said patron soul-jarred him, then used a continuous flame-jet on his body. Said patron then used a resurrection spell, and put him back into the reconstituted (but naked, unarmed, and healthy). Turns out the guy seems to be a jerk in most contexts, but he;s just one of a dozen such people I've encountered in >40 years GMing.
The creative tools are, usually, not for the players, but
for the GM. Traveller has them aimed squarely at the ref (GM), but uses the coded output strings for both character use and for ref and player knowledgebases. (The strings to describe a world are, canonically,
in universe shorthand. Likewise, the strings for characters' attributes appear in the supplement 12 in-setting ID cards...)
Examining the best known such tool, Traveller's world generation (only mildly changed in even the newest editions, excepting and ignoring the ports to GURPS and Hero)... Creating a single world is a big challenge. Creating 10 to 40 of them? daunting. Creating the average of 300 per sector? at best, you get swathes of similar worlds. Which is where the random world gen comes in: I can bang out a subsector in an afternoon, with a couple senteces per world, inspired by the string of physical and social data (Startport Class, Diameter, Atmosphere, Water coverage, Population¹, government type, law level, tech level, presence of bases for the parent interstellar polity, presence of asteroid/planetoid belts, presence of gas giants, and in later evolutions, stellar type.) In the end, it's allowed me to riff world differences much more easily than if I were to create them all from scratch.
Now, Brad Murray's
Diaspora uses a different process, but has a system for generating a cluster of worlds, and the worlds themselves, to do likewise... but shifts the rationalizations to group rather than GM alone. Mostly due to the consensus standard that Brad's games employ (final authority is group as a whole, not GM, in all of the games of his I've read.) It works in a similar manner - a short form rolled mechanical description, which serves as a springboard for the group to provide details inspired by it. Less random, more group labeling of new traits, but still, the idea is that it provides a spur of the imagination and a shorthand reference. (While I've not run Diaspora, per se, I've used its rules for solo activities other than in-character play, and used many of Brad's techniques in some Traveller campaigns.)
That said, many games character generation rules are inspirational/evocational... most notably, again, Traveller (with it's career based path) and Cyberpunk 2013/2020 with it's low-mechanical-impact lifepath... but also any game with purely randomized character gen (WFRP1E) or random atts with a few choices following (D&D pre-3E, Palladium, Traveller except the ports...)
