I feel like 5e could be GMed with a more story now approach. I don't think it's strongly suited for it. I think the adventuring day "budget" and the short rest/long rest recharges are where the strongest opposition would be.
But I don't think it's something that can't be done. I feel like I've GMed with this general goal in mind in a campaign my group was playing that went on hold at the start of the pandemic. I'm sure if I could look back over a transcript of play, there would be points that clearly failed the sniff test, but I don't think it might be as many as would be typical in 5e.
I think if the GM and the players are approaching play with this mindset, then it's possible.
I wonder if there are types of campaigns or even types of individual sessions that might lend themselves more to this approach. For example, urban campaigns where combat is deemphasized (because of the context of the city). The problem of how to "crawl" a city is complex enough that it can lead to a more scene-based approach. For example, this product is interesting in providing encounters for PCs as they wander through the city. Ostensibly, they have a destination in mind (as related in the Waterdeep AP), but I can imagine a session that just introduces an encounter, keeping in mind the fronts/factions at play in the city, and letting things snowball from there. (This take is somewhat inspired by this podcast episode).
But, dnd being games not one game, it might be the case that style of play various from session to session, or even within a session, and so things become blurred.