very fair points, I’ll concede Burning Wheel is not a perfect example of what we are talking about, but I will say the tag system is more flexible than you assume. Yes, having the “big hat” tag will provide you a bonus to the scenario provided, but not having the tag is not a no-go. If you narratively position that your character had procured a big hat, you could convince the GM that they can use that hat for a one-time bonus, and if you consistently rely on it, there are mechanics that let players nominate you for the “big hat” tag at the end of any session, at which point you get more control over when you can invoke the tag.
To bring it back on topic, I think BW has better GameFeel than DnD because while its mechanics are less dense, they are also more rigorously defined in what they are meant to simulate (both by explicit author writing and in what “flavor” the mechanics are given). You could can run a game involving a group of characters travelling a fantasy world and building bonds to achieve some lofty quest in either game, but BW will do it better (opinion) at the expense of doing less things than DnD (ignoring how well DnD does those additional things).
I think there is something to be discussed in how much lifting “genre” or flavor does towards reinforcing mechanics. If Night Witches was pitched as a game for playing as pilots (no era specified) it would do what it was designed to do just as well but would be more difficult for players to “tune in” to the ideal play style.
Perhaps the difference between indie and classic design is how much genre is defined versus implied by the mechanics? Night Witches lays out what it’s about very explicitly, which does wonders for helping players enter the desired headspace. DnD and BW rather define their setting through the content. DnD definitely assumes the name is doing a lot of heavy lifting and BW’s rules only imply (there are rules for hitting people with medieval weapons, casting spells, and creating characters of different fantasy races), but I don’t recall it outright saying “this is a game for LotR style adventures” beyond listing LotR and other related stories in its bibliography.