That, more or less, is how I do it, every single time. No complaints yet. Everyone's happy. This is how I've done it for the past 20 years.
If you don't do it that way, that's fine. You do whatever works for you and your players. This is what works for me. The reason it works for me is, mainly, because it plays to my strengths. I am a storyteller, so I'm at my best when I'm, you know, telling stories. That doesn't mean "railroading." At least, not the way I do it. Railroading is when you invalidate the players' actions in order to tell your defined, set story. I don't do that. I meld the players' actions into the story, when possible. When not, I follow the players' lead, see where it takes them, and look for opportunities to meld their actions into the story. This isn't really the popular way of doing things these days. But it works for me, and it works for my players.
Of course, when I'm at my very best, my story isn't completely defined. It's got points A, B, and C, but I let the players draw the lines connecting them. One of my favorite adventures, one that I've run multiple times over the years, is a scenario I call "One Night in Innsmouth." In this adventure (I've run it on three different RPGs), the players choose one of four different reasons why they're going to Innsmouth. Then, after a few scenes of poking around, the sun goes down, the town starts crawling with Deep Ones, and the players are fighting for their lives to escape the town or make it to sunrise before they all go away. (I frame this adventure as an "unofficial sequel" to Lovecraft's classic story "The Shadow Over Innsmouth.") Those four different reasons, they each have their own particular details, but really the most important part of the process is this: which reason they chose determines where in Innsmouth they are when the Deep Ones come. That's it. The story is really just whatever happens while the players are trying not to get sacrificed to Cthulhu. So the story has a definite beginning (players arrive at Innsmouth for a reason), middle (sun goes down, Deep Ones everywhere, players trying to survive), and end (the players escape...or all die). But what happens exactly within the beginning, middle, and end of "One Night in Innsmouth" is all on the players.
Here's another one. I did an adventure for the Firefly RPG once that started, in TV show fashion, at the end. Each player's character was in a loaded, action-packed situation and they didn't know why: one character was dangling out of their ship while it flew through a canyon; another was in a crate full of peaches; another was holding the ship's pilot at gunpoint and forcing him to fly. I then played the Firefly TV show's theme, and after the theme, the adventure began with "earlier that day..." The rest of the adventure was just setting up events for the climax I "cold opened" with. Again: structured story, built around the players' actions.
I call this approach to adventure design "liquid metal." Sturdy and tough, yet flexible and fluid. Like the T-1000 in Terminator 2.