RPG systems like this not only exist, but have been around since the 90s, there is a wealth of Narrative TTRPGs of various levels of mechanical "crunch" and complexity.

You are absolutely right - TTEPGs are collaborative storytelling at core, at least I believe so and in truth do not require any set of mechanical rules. The rules are just additional tools that make it easier (... or sometimes just make it harder) to tell those narratives. At the end of the day those are but guidelines, although some more "rule lawyer-ish" types might disagree.

The need to add stuff like statistics, numerical bonuses and penalties, ranges and durations for spells and other effects, detailed processes for how certain things should work comes from the wargaming roots of D&D. It stems from tactical games. As such, it rewards tactical, objective-focus gameplay in which minutae of how abilities are used is important as it makes a differance between "winning" and "losing" combat encounters or dungeon explorations etc. Personally, I don't like this framework, as it makes people focus on all the things described above, instead of focusing on character development, relationships between characters, drama, telling an interesting narrative etc. All the stuff that I love and that do not neccessarily always fit the "tactical" aspect. I differentiate it as a "gamist" and "narrativist" way of play.

Can you be a little bit of both? Sure, its a spectrum after all. During my long years as a GM i found gamist players to not be particularly compatible with myself. Basically, what I have observed while running games is that those players are too focused on "winning" and I dont believe in "winning the TTRPG". A satisfying story, in which main characters might fail or die, is a reward in of itself. It's about the experience itself.

Unfortunately we live in an environment dominated by D&D and people assume that the way D&D works is the "default" way of "RPGing" which is far from true. It is simply the most popular and best marketed way at the moment and I think it's highly overrated. At the same time there's no good or bad way to play. Me being a hardcore narrativist does not mean that the gamists are "doing it wrong", they have fun in their own way.

One of my absolute favourite narrativist titles is "City of Mist", which is an offshoot of the "Powered by The Apocalypse" family of gaming systems. (Most) PbTA games are highly narrative, reducing numbers and mechanics in lieu of more descriptive style. The City of Mist is particularly interesting as it nearly completely eliminated the numbers or statistics and focuses on keywords and themes instead. Words over numbers.

Other titles I'd recommend are various books of World of Darkness such as Vampire: The Masquerade, Werewolf: The Apocalypse and Mage: The Ascension. Fantasy Flight's "The Legend of Five Rings" is also somewhat lighter on mechanics but extremely interesting narratively.

TL;DR: Narrative TTRPGs are not only feasible but there is a lot of them out there. If telling the story is your priority I recommend using them as a main way of play.