I'll take this one step further in a way that I hope is productive: I think this is the approach to play that D&D supports the best. Or, if you want to play a game like this, D&D does it better than most. Or maybe both. Perhaps I'd say that at it's most pure, D&D is a sandbox (even if the sandbox is just a dungeon) in which the players have a great deal of control over the challenges they pursue, the risks they take, and let the dice fall where they may. If you succeed, you level up; if you die, you start over and try again.
For me, that's the sweet spot with D&D. I've gone through phases where I wanted more strongly narrative games with multi-page character backgrounds and some form of script immunity, and I generally found I preferred the way other games supported this style of play. I've also been through phases where I felt that RPGs in general are a lousy medium for storytelling, and that what you get in reality are clichéd characters, pastiche settings and incoherent plots that would be embarrassing in any real literary or dramatic media.
And that's key: Even for me personally, there's never been "one true way." My preferences have changed and changed back again over 35 years. Do whatever is fun for you and your group, and realize that you may change your mind tomorrow. Don't take it too seriously.