I think Dungeon crawling is a big part of a LOT of fantasy we consume, whether video games, movies, television series, or books.
It just doesn't necessarily look like D&D dungeons, and tend to be less designed like 1986's The Legend of Zelda's underworld labyrinths and more like 2017's The Legend of Zelda: Breath of the Wild's Hyrule Castle: open world exploration of cities and ruins etc.
D&D has a heavy dose of Indiana Jones in its DNA, and that's not a bad thing.
Certainly when it's all about dungeon crawling or getting from the end of one dungeon to the beginning of another, the game starts to lose it's grounding in when compared to modern fantasies (I compared Zelda before, but most fantasy stories outside of the video game medium do not send the party to go gather 3 magical stones to get a sacred sword out of a pedestal and then 6 more magic mcguffins to unlock the seal to the big bad's lair).
Most fantasy series do have a driving plot, and often seek for a sweeping view of a country, continent, or fantasy worldspace to give a taste of various different morsels. This means that the outdoor exploration tier tends to be heavily represented in fantasy fiction, but D&D's dungeon-crawling roots aren't as well suited/adjusted for "The Fellowship Travels Across Country" portion of the game.
Unfortunately discontinued (at least for the time being) TTRPGs The One Ring and its 5e-compatible adaptation Adventures in Middle-earth provide a useful feature to the game that tracks the sorts of challenges a company or fellowship might face in the wild and how they might work together over large scales of time and distance. It's a good idea to zoom out when exploring, only to zoom back in for the occasional wolf pack or bear attack when relevant.
When I play Breath of the Wild, most of the adventure is just me and my wits and stamina against the elements (most often against the rain, darn slippery rockfaces! But also against the cold of the mountains, or the heat of the desert or volcano, or the darkness of a forest enveloped in magical night). In a given playthrough I might run into some bokoblins/keese/octoroks/chuchus, or moblins/lizalfoes/lynels/hinoxes/moldugas if I'm unlucky or venture into dangerous places, but most of the time I can explore safely, or find a safer route around the problems so I can focus on my fruit, veggie, bug, and mineral collections, or focus on making it to that next major landmark or far off in the distance.
Exploration Pillar needs a lot of work. I don't think D&D has an inherent problem with it, but the game does a very decent job explaining the combat encounter, how magic works, and dungeon crawling, and a decent job of explaining social encounters and how background characters tie the characters to the plot, but a really poor job explaining everything in-between, especially when it gets to large expanses of time and/or distance.
I think trying to load that pillar up onto the back of the Ranger was part of the problem (and why the Ranger is seen as a poorly-designed class, as written in the PHB, at least). I think a lot more heavy lifting could be done by the core rules themselves.