Yeah, this right there probably explains far more than anything else.
Your campaigns run about twice to three times as long as mine do.
That's unfortunate, Hussar. Of course, I went through a period where even getting in a single game of D&D was impossible. I've now got two pretty stable campaigns; although neither could be strictly described a sandbox. In fact, you could definitely say one of them isn't; the other one has the potential, but isn't.
That second campaign - my Greyhawk homebrew - is a fascinating study. The players who participate in it aren't comfortable with driving the action. When it comes to the goals of their characters, there are none that are apparent as regards the greater campaign. At times they seem content to drift along, seizing any chance to adventure as offered by me the DM.
Meanwhile, the more successful campaigns I've run have been ones where I've driven the action, for instance: the land is under invasion by the Fhoi Myore... you need to stop them. In theory the players have the ability to go where they want and approach this in the manner they need; in practice, it ends up as more quest-driven where the quests come from me.
Thus, I set the parameters around the adventures the group goes on; their character motivations are "save the land", "go on adventure" and "be with my friends", but the genesis of the adventure is fully in my hands.
Meanwhile, another of my successful games, although it did have a lot of the DM-determined quests in it, also had a player who was very active for their own motivations: she wanted to gain power over people. When the opportunity came for her to gain status in a town, she took it. The adventures I then designed were reactions to her actions. (You've displaced the local lord? He comes for revenge. You survived his revenge, and now you want to face him in his lair? Well, I'll design his lair).
I couldn't describe the campaign as pure sandbox, but elements of it were certainly of that nature, and this part was very player-driven.
The level of engagement in that latter campaign with the elements of the campaign world was very high, needless to say.
However, and relating back to the levels of engagement in my original post, is it necessary for adventures to be derived from player action for the highest level of engagement with the campaign? I think the definition of "highest level" is fuzzy enough that you could define it as the answer being either "yes" or "no"; so a definite answer isn't obvious.
How much does it matter if a game's adventures are DM-driven or player-driven? Is this something that is actually more dependent on the dynamics of the group rather than something we can make definitive statements about? The more I consider it, the more I believe that might be the case.
Cheers!