I don’t think you’re being fair to the published Campaign Books. All a campaign really is, are a series of linked adventures. Connected by theme, location or overarching plot. Most campaigns that I have seen run around a set home base or a set rising threat.
Princes of the apocalypse is a set of wildly disparate locations that link together by having a theme to the enemies but they are all very different, as are the towns and villages in the Sumber Hills. It isn’t one story there are lots of enemies and the PCs pierce layers to reach the bigger villains further on in the campaign.
Out of the Abyss is a series of individual encounters/adventures set in the underdark and the theme that demon lords walk amongst us. The locations are all very different and are really a set of separate adventures.
Similarly curse of strahd could easily be viewed as 14 separate adventures linked by Strahd himself and the setting.
In all three, players can interact with the story however they like, the DM can chose which hooks to feed to the players and which section can fill which gap, cut things out, alter things etc. I really don’t see how it is any different to a DM stringing 3 adventures out of dungeon magazine together in a home brew setting.
I'm not saying that they are bad. And I, for one, have enjoyed the fact that each one of the APs has been written with a different design approach.
Although OotA has a lot of different adventures, they are all ultimately leading toward one final conclusion. The AP doesn't have a lot of potential alternate story lines should they decide to go a different direction, nor is it designed in a way where different groups of characters could easily play out different parts of the story.
***Possible Spoiler Alerts for Out of the Abyss***
For example, let's say I as a DM decide we'll run OotA. The players make their escape and are into the Underdark. From the book "The adventurers must find a way out of the Underdark and back to the surface world." First off, why? Why aren't there other options? Why aren't they able to determine who enslaved them, and possibly take revenge? Regardless, the book goes on to say that their fellow former slaves know how to get to other places in the Underdark, but can't help them get to the surface. And if left to their own devices, they wander until they find somebody that can point them in the right direction for the AP. That is, there is no consideration for an alternate story line. There are subplots, and lots of variety, and they are for the most part really well written adventures. But I wouldn't consider them campaigns.
End spoilers
To me, a campaign is more than just stringing adventures together. It's more about providing the setting for the adventures to take place in, an ongoing setting with the stories of lots of games and lots of adventures. The players through their PCs have more of a say as to what they do, and what adventures they choose. The original campaigns were things like the Gygax home campaign, where lots of players had lots of characters dropping in and out, developing the setting and some of its stories as they went. The Greenwood Forgotten Realms campaign is similar.
Really it comes down to the players/characters being able to explore the setting, to "write" alternate stories, rather than the one provided by the AP. While you can rearrange the parts of the APs in any way you want, the overall plot remains the same.
It's really more a matter of tools. A DM with an established campaign can react more easily to players "going off-script" while a new DM that doesn't have anything like a campaign, or experience in dealing with it can run into trouble. Especially if the players decide they don't want to pursue the main plot at all. The APs generally give advice on how to get the PCs back on track, that is, to follow the plot. The article linked in the OP was commenting that the APs are too sandboxy without providing the right tools for the DM to handle that. I think that's partially correct. I think they need to provide better tools, but that they aren't too sandboxy. The tools that are lacking in this edition are those that help flesh out a campaign.
Even the DMG isn't really a help here. It talks about designing adventures, and has pushed the stuff between adventures largely into downtime. But it's the between adventures stuff that is needed when the PCs go off-script. New DMs aren't typically prepared to improvise, and especially not when the PCs decide that they don't want to follow the overarching plot at all.