Players who have issues with APs usually have the same issues with any mod-based campaign: if closer the DM follows the adventure as written, the more story centered the game becomes.
Is this bad? No. Can some people find faults in it? Yes.
When you ask someone if they want to play D&D, there are, IMO, four iconic campaign styles to play:
Story Driven Campaign
Examples: Adventure Paths, Modules, RPGA
Advantages: Players can usually easily come and go without affecting upcoming plot arcs, gameplay is generally balanced, the story might motivate players to see it to the end, excellent for meeting new players in a more formal atmosphere
Disadvantages: Player character backgrounds have little to do with overall plot, generally little room for freeform exploration, some players might not like the story
Exploration Driven Campaign
Examples: Forgotten Realms Campaign Setting, Eberron Campaign Setting
Advantages: Players can usually easily come and go as the focus is more towards the world rather than the characters, players are free to explore a dynamic world that isn't catered to their party makeup
Disadvantages: Players may disagree on where to go, player character backgrounds are not always center stage, the world isn't catered to their party makeup thus they can explore areas that may be too dangerous for their party, a general lack of metaplot that guides players where to go
Character Driven Campaign
Examples: Complete Series, Races Series, PHB 2
Advantages: Players almost exclusively determine the metaplot based on their character creations
Disadvantages: Difficult to deal with player absences and new players, player background conflicts can result in arguments over metaplot direction
Action Driven Campaign
Examples: Dungeon Crawl Classics, Expedition to Undermountain, Fantastic Locations
Advantages: Players can come and go, metagaming and min-maxing can be encouraged, different levels of play can be introduced at any time
Disadvantages: Players may complain of shallow roleplay experience, exploration is limited to the dungeon or plot railroad, few non-combat decisions
If you're going to run an AP, players need to understand that you're running one. One person might be expecting a game where the group is going to return to the Underdark because a player's character was exiled from there, another might want to see a big map of the world and ask questions about the best place to hunt for dragons, and another might just want to try out a 11th level dread necromancer one week and then see if a 15th level duskblade is balanced the next. None of these people are going to be happy if you say "Hey let's play D&D" and then start them off in Cauldron at 1st level. Explain to them that you've chosen to run a story driven game, and make sure they understand what that means.
I'm very lucky to have several opportunities to play multiple types of games. When we could only run one campaign, I chose APs (Age of Worms), because it was easiest for me to run and my players wanted to play it to the end.