As an aside, many of the TTRPGs that are, rightly, lauded for having great (or, IMO, "tight" design) accomplish this precisely because they are limited.
The more you institute constraints on what the game is about- force the genre, force the processes of play, force the methods, for the acceptable playing styles, force the ways that the GMs and the players can interact through proscription ... the easier it becomes to make the rules more complete.
This is neither bad, nor good, but it is a salient feature of design that I have observed.
Again, IMO, YMMV, etc.
Exactly. They're all RPGs because you're playing a character, but they are clearly different kinds of RPGs. Different genres of games, but not in a fantasy vs sci-fi vs pulp sense. They have different design goals. This one's a survival game, that one's a 4X game, that other one is a shooter or beat 'em up game.
While not generic, games like D&D and Pathfinder are more...broad...more like life sim games. Where you're meant to inhabit the character more, I guess. And the mechanics try to cover (almost) everything you can do in that character's life. Which leads to sprawling design and a voracious need for ever more rules to cover things and ever more complicated subsystems.
I prefer to have that part already done, which is why I'm willing to put down money to use game systems that set those things down in terms of rules, presumably designed and play-tested by people better at creating games than I am.
As a player there's no difference except saving the money. You have a document to reference.
The referee at your table running that FKR game just might be a professional game designer. No reason to assume they cannot be trusted to design things. Further, no reason to assume the stuff the pros put out is inherently better than everything else. I've bought professionally designed stinkers. I'm sure you have, too.
The idea is that if having written rules leads to debates about their interpretation, having no rules except for what the referee comes up with has the potential to be even worse.
Worse than what? The people at the table arguing about what the book really means? Okay. How are those arguments usually resolved? The referee makes a decision and the game moves on. So, why do you need the rulebook in the first place? You don't. If there's any question, the referee makes the call regardless of what the book says. The referee is the final authority of the game. What they say goes. Not the rulebook. You trust them to make those calls. If you don't, don't play with them. It's the same with FKR only you save money by not buying an overpriced coffee-table art book. Spend that on movies or novels or comics instead. Use those as your reference works.
While I think that "mother may I" is an unfair way of describing a lot of games rely heavily on referee adjudication, the underlying idea is one that I'm sympathetic to, in that having an impersonal set of rules governing what can be attempted – even when those rules are unclear – can be more empowering for players than having a single GM who determines everything.
It's an illusion of empowerment. The referee still makes the final call regardless of what the rulebook says. The rulebooks also specifically call this out with whatever variation of Rule Zero they use. The rulebook cannot protect the player from the referee. Never has, never will as long as there is such a thing as a referee making calls.
Take 5E as an example. The referee still sets all the DCs, still determines all the monsters that show up, how all the NPCs act and react, etc. Yes, you can point to the athletics section of the Strength ability rules to say this or that, but whether your athletics skill is relevant or not is up to the referee. Whether the DC of that athletics check is 5 or 50 is also up to the referee.
It also seems like less work for the GM as well.
As someone who's actually done it, you'd be wrong. It's orders of magnitude
less work.
Again, it's not all about trust. Genuine disagreements can arise, and when those happen it causes less tension for the group (in my experience) to be able to lay at least some of the blame for that on unclear rules than to make it entirely about a clash between two or more people. Written rules act as an insulator in that regard, to the point where you don't have to rely on trust in the first place, and I think there's merit in that.
Again, it's an illusion. The referee still has to make final the call. And either the player trusts them to do so or they don't.