I used to think that doing so was more work for the DM, and that it was beyond my skill as a DM. The funny thing is that once I actually gave it a whirl, it was the most natural thing in the world. It's what we, as DMs, are already doing. At least unless you're following the written text of the adventure in lockstep, which I don't think happens outside of the very most inexperienced DMs. It's like if the party decides to walk through the dungeon loudly banging pots and pans together; do the denizens remain static in their rooms waiting for the PCs to enter, or might they come out to investigate what the noise is about?
This is just going one small step further and giving a quick thought to what the wider implications of the PCs actions are. It's what every DM has to do if the PCs go even slightly off script (assuming there is a script). It's simply thinking 'The PCs did X; what happens as a result?'. I'd been so daunted at the prospect of "creating" a dynamic world that I never broke it down into its components to consider how it worked. Once I did, I realized that it was really quite simple; I'd effectively been doing it all along, just restricted to a smaller scope. Since the campaign world exists primarily in the mind of the DM, changing your scope isn't hard to do unless you convince yourself otherwise. It's nothing more than making stuff up for the entertainment of the table. IME of course.