You're right in that I largely do disagree with that stance, mostly because when I look at an RPG system my first (and maybe only) thought is whether I can kitbash it into doing what I'd want it to do. Big-tent systems have an advantage here as they're already intended to be somewhat flexible, but I've found - mostly through converting adventures from other systems to run in my own game - even there some are much more flexible than others.
The problem is, the stance of the game towards PROCESS, who gets to say what, how, when, is baked into every subsystem in the game. Its not something you can 'kitbash' for. Anyone can graft another subsystem onto a game, or remove one, or rewrite all or parts of one, etc. What you CANNOT do, in any significant sense, is to reconstruct 5e (for example) as a narrativist game. It just ISN'T.
Nor, from my perspective are these trad systems, particularly 5e, all that 'big tent'. 5e had the chance to simply leave in place many of the narrativist innovations of 4e. Instead we were literally hurled out of the tent on our asses! I wouldn't say that reflects on other RPGs in any sense, but here I am... Honestly I can't blame them, it just isn't possible to revamp the core level of how the game is structured, from a play perspective, and not end up with a new game.
I would far rather just learn one system really well and then make it work for whatever I need than learn a multitude of systems bespoke to each play style.
But, from my perspective, your play is a pretty narrow slice of RPG play, so its not surprising.
If you're not a kitbasher and instead just want to pretty much use games as written, then System Matters clearly makes sense.
I've played D&D since it was 3 little brown books and called "Dungeons & Dragons", nobody needs to explain to me about 'kit bashing' etc. Heck, when I was 12 and I couldn't get a copy of the rules, I just wrote my own. This is not about whether you can or will adapt games, its about there's fundamental core differences between these types of games.
Now, like 4e is based on 3e, you can go from trad to narrativist with a rewrite and keep a lot of elements, if you are not worried too much about changing what they do, why, and how. But they are pretty different, and clearly 3e fans noticed that!
So, again, advice, use a system that is intended for what you want to do. I'd rather adapt a narrativist system like a PbtA to an entirely new genre than try to force D&D to do narrativist style play.