Never said this, but using extremes to try and make your point is always effective...
Then I'm not really understanding your point. Because you did say that the DM does not control the pacing.
Weren't there random monster tables for the wilderness around the Keep on the Borderlands which is the actual "sandbox adventure"... or are you equating a sandbox adventure with a single dungeon that's only a piece of it? But ok, just looking at the single dungeon... every room is keyed and yet there is no guarantee that the PC's will face a particular monster in a particular room or at a particular time (where and when).
I've never heard anyone distinguish parts of KotB as being sandbox and other parts not. I have heard it described as a sandbox adventure. And, while, yes, I believe there are random encounter tables for outside the Caves (and inside as well), there are ALSO a number of keyed encounters around - the mad hermit, the lizardmen, The Cave of the Unknown.
How often he rolls on the random encounters still doesn't guarantee a specific pace, so he's not setting anything... If anything he can influence when and how often encounters occur but they will still be subject to randomness. If he's tailoring encounters however, yes then he is setting the pace.
Specific pace =/= setting a pace. If I roll 1 check every 8 hours, I will get a VERY different pace than if I roll 1 check every 10 minutes. Yes, it's random, but, the DM is STILL setting the pace.
I think the characters have as much or as little control over pacing as the actions they choose allows. You're assuming that most of the time PC's are flying blind... when in fact this is again a function of the PC's chosen course of action. Exploring the setting =/= flying blind... not sure what sandboxes you've played in but that's just false. Research, information gathering, etc. are part of that exploration if PC's choose to make it so.
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Most of the time you are flying blind in a dungeon. After all, other than, "There are orcs in that there cave", you're unlikely to have a whole lot more information. When faced with a T intersection, left is usually as good as right. Granted, there are ways to make this not true, but, broadly, the players have little specific information to go on.
And, if encounters are all randomly generated, what information could they possibly be working with? After all, there's nothing to tell them when or where they might meet something, other than, I suppose, there's bad things in that forest - you might know roughly what to expect. But, you have very little control over when.
Thus, very little control over pacing.
Isn't it funny though. When people talk about the 15 minute adventuring day, it's up to the DM to make sure that they cannot rest whenever they want to. But, in a sandbox campaign, players have total control over pacing. Which is it? If I have total control over pacing as a player, then I should be able to rest whenever I want to.