Clearly different DMs have different experiences with the utility of published adventures. So what predicts whether or not using one will save you time as a DM?
I can think of two possibilities. First, if a DM tends to do very little prep work, than even reading through a published adventure takes more time than allowing spontaneity and the players' input to drive the content of each session. Personally, I'm not nearly good enough at improvisation to pull off this approach to running a campaign.
The other possibility is that the adventure as published is not immediately useable for some DMs: it requires work to "finish". Perhaps the content of the adventure book isn't what a given DM would have included in their own notes if they had started from scratch. For example, H1 is full of monster stats, tactics, and terrain, but it gives little guidance on how to imbue NPCs and individual monsters with personality. From an adventure design perspective, perhaps a DM would never have made the dungeon so large, so he or she must invest time in pruning encounters while maintaining the overall story and while adjusting the later encounters for characters who won't have gained as much experience. In the most uncharitable sense, it could take more work to "clean up somebody else's mess" than to do it yourself.
This second possibility is closer to the truth for me, although I still find that using a published adventure is much faster. It's just the case that I personally can't just open the book and run it without preparation.